Best Known (105, ∞, s)-Nets in Base 27
(105, ∞, 324)-Net over F27 — Constructive and digital
Digital (105, m, 324)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (105, 323)-sequence over F27, using
- t-expansion [i] based on digital (72, 323)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 72 and N(F) ≥ 324, using
- F4 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 72 and N(F) ≥ 324, using
- t-expansion [i] based on digital (72, 323)-sequence over F27, using
(105, ∞, 325)-Net over F27 — Digital
Digital (105, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (105, 324)-sequence over F27, using
- t-expansion [i] based on digital (48, 324)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 48 and N(F) ≥ 325, using
- t-expansion [i] based on digital (48, 324)-sequence over F27, using
(105, ∞, 2793)-Net in Base 27 — Upper bound on s
There is no (105, m, 2794)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (105, 5585, 2794)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(275585, 2794, S27, 2, 5480), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 33609 210463 315024 187049 762822 563276 465602 874439 169916 266116 388291 908352 322604 401105 651494 727020 643501 754822 738190 136994 859555 671346 791941 545926 070054 984346 714605 973338 817469 249689 206111 178157 739004 371471 192816 785243 247333 577553 075993 895839 413910 623276 125356 794482 478467 907443 184335 469153 158082 766925 746264 294387 951877 822057 230304 286740 921525 510621 480164 802894 244792 116637 359665 854738 601242 725813 744960 539413 168582 215018 037925 390419 997868 965227 026311 357979 824040 659057 660784 920297 604245 575410 930088 798646 106088 493230 198107 326498 424742 009898 576078 590330 280583 302533 844205 654653 263091 551105 372052 014231 357736 097566 836470 107011 909964 444398 996524 091088 995950 495023 357301 688603 288741 297082 001859 446963 079585 015676 272515 125415 513432 569292 514907 367474 186561 007644 563508 918337 865362 296143 279362 586214 675198 255237 855744 480555 298219 830939 128180 312174 034057 248696 304398 244821 877388 772659 508042 162046 117165 392313 929011 719171 024978 370053 049209 420781 589646 384964 685984 630439 013569 663870 817964 324900 671620 279651 430675 451839 245473 087403 408863 920564 165953 296597 583309 583485 219118 302090 446272 697894 882817 995966 936988 850945 962679 628055 584236 811989 081993 339235 006137 725102 425515 526602 729154 618370 360928 421394 795569 993492 586001 734943 186777 531782 262095 375556 897032 074114 133754 157796 519093 219979 958759 557801 451515 650177 200019 447966 849052 419713 794921 496147 944818 423209 280384 834866 641995 776313 378449 234518 352080 496868 865485 429539 992806 446064 127893 248707 174515 531557 082665 598532 842572 159872 071564 609136 256791 849263 463954 388953 693135 766900 038994 771045 871971 182537 704228 543992 013453 249020 381778 373461 546400 465238 477903 516201 703986 580192 611548 946068 265109 474514 793583 914609 387252 868487 194227 727419 882707 303417 765582 336427 994038 428883 958279 549805 465469 346296 595128 245223 932821 465605 859663 397500 333737 254803 652951 268544 074864 568298 533631 534645 366500 607484 615739 917449 826600 843058 076796 514455 540702 415183 939633 668146 330431 413064 855961 103909 362468 988871 677788 973127 215075 912614 420550 814851 330992 518087 858866 752480 697927 705283 271627 202690 132491 998323 539686 092633 787574 470357 247016 123535 189169 779371 341399 840399 409633 720400 401958 007811 840719 176235 386766 767781 265809 804694 984359 204143 851479 560756 916079 936436 278545 703441 665443 829668 087701 167749 280020 840337 016990 879770 283712 702419 340753 120679 243019 030710 005978 340499 368469 194666 579473 071243 035331 131241 225494 360418 153088 844420 215273 763844 649850 609750 925358 659155 243974 626905 392629 619532 012265 836232 691144 257836 987185 167343 433417 717268 584106 914122 136428 104937 690217 626590 790446 682481 159713 170564 018112 311569 330988 579728 806237 169860 796454 467288 643810 937582 555435 682596 767840 600832 776505 647828 623326 302534 939876 927379 373926 220991 808458 302098 693616 327980 636701 886180 096897 063070 569252 887796 284085 310163 992228 730431 603950 212599 309497 077650 451326 894991 932513 435917 264657 681322 709093 493791 511058 759797 934500 375150 760118 558301 611045 970042 438615 356594 751129 896050 100793 721601 217487 567378 240284 899166 029856 920256 261744 569030 273008 463687 172496 553774 149387 439151 836647 688502 684571 223077 915504 090734 700318 443401 076768 798281 147014 832396 282883 204280 533843 780561 897066 718583 605878 881350 001167 473987 413895 015735 392936 466023 213226 643099 953689 848334 826630 879759 791439 726887 889350 424853 968058 387983 850013 997478 425868 026949 557182 243592 559463 741146 886535 042695 219875 881808 547157 917326 490486 872968 400938 225249 016934 780453 275968 660403 056157 199107 100849 730080 110456 820453 380422 825454 996199 493548 961291 922627 372662 096286 171195 991069 961543 690041 120048 483263 687685 264838 595258 306775 890683 450166 838856 462153 172491 370320 663636 613233 344629 109752 224799 273596 539726 858830 727822 804583 368125 683082 125845 485783 958238 275764 905666 120197 935911 049669 724131 422079 250962 974334 285292 835089 110081 797438 038144 133401 345938 774975 641859 910848 750206 545933 633045 512850 770925 236478 594690 481497 377074 059765 025130 319754 247863 009472 938070 095458 297417 959183 037965 492515 530834 052959 642796 139170 706543 198998 675212 989232 412050 278043 081754 936472 320027 515137 687624 932526 867870 223716 976721 653809 972888 269180 415214 675544 985794 886719 902626 898192 665908 197262 662513 259312 411347 591925 451639 629230 374899 024595 242612 518635 709866 238605 098128 558057 876143 745030 597351 389364 401698 872068 867751 207436 754864 553401 969769 253707 307881 438828 125996 243123 864988 000726 191967 003568 578897 218190 660295 501643 722755 015999 164653 913241 636672 722478 660725 422932 498773 221483 427535 981078 516600 717364 756314 035623 808124 176614 374817 481646 864848 029515 876253 437957 979526 469123 695840 800972 736522 495533 136270 989842 615695 221767 948906 544079 734942 765213 001302 698783 902612 887890 611200 468082 504739 699279 870772 341378 322286 141798 692531 011835 281748 621781 770411 583502 625809 798862 111255 270705 694462 463019 123217 374458 492631 244858 544388 690375 280612 493560 811715 776199 694017 356738 424406 663447 614168 272529 110987 682371 742019 758130 732379 327514 588518 215731 528787 680274 777018 525213 782806 937918 385273 818749 872169 251573 091321 839574 627264 170018 942757 448760 199512 605461 833750 638480 763413 959892 532362 378396 215979 616529 596449 372599 230121 710040 488505 853237 354692 007200 000446 923613 745820 412569 381256 007965 825540 501059 051132 153638 922767 505327 721390 306460 776162 475086 872261 434005 341318 384063 249856 424186 476058 644741 914855 939088 848558 829810 343838 504765 111528 365416 367331 486707 905091 854852 844456 796815 134809 833061 315817 230412 598936 955508 565536 415179 079353 225061 357393 332906 077800 865677 116329 360253 692598 967986 141922 303925 368164 013376 172544 243421 242939 586933 499114 014084 893983 569378 232127 327720 278534 472183 036864 426582 047018 093996 962326 385413 012493 572581 204336 081638 126665 143824 365169 604382 888947 473617 201908 784554 616527 304204 010901 826937 164390 863964 233655 209892 894384 203959 325161 890297 677242 587063 957948 826613 662855 142184 029955 791055 332962 028392 164257 430959 645188 913492 317388 496191 756164 278443 928914 649778 335919 876635 441649 251011 333168 144494 538591 685377 183408 873168 479915 726582 461219 515992 550891 932683 784764 994843 917575 777060 086080 856932 321868 769120 683532 401242 021391 764444 874759 992679 407245 048848 645078 489905 332102 147801 608860 962309 918194 110207 716539 089116 878354 230271 200863 434329 432240 315592 524754 900888 570287 412308 466599 528435 058957 980205 246333 983006 145373 795326 767938 678580 714259 383221 680067 315167 747972 449374 770768 483686 946982 256087 339959 520351 819878 386427 620282 504114 532862 687045 347391 129678 071705 824996 969436 347413 242430 619422 551607 225443 640850 156903 915230 894579 132800 732933 765404 570459 563272 317393 350570 209553 051850 023921 873973 372811 446286 022384 898411 950485 029432 627405 902984 489069 394713 452421 834092 320880 793784 451306 622431 530682 386581 724563 093507 501538 998618 539862 085125 970885 357813 575620 912959 933329 018013 261896 323963 799849 292109 425735 636588 944186 764731 265737 823754 751460 633937 283900 537857 133732 380457 022203 108407 147355 537632 118486 694646 551138 608179 947424 630866 690056 811819 522988 724086 758329 384470 195374 323255 883337 632158 518586 738191 386626 378741 114402 775606 762630 849319 666799 277019 481118 117776 603746 716631 799382 967558 164149 159703 653693 166428 898108 943643 552677 923700 175951 556013 975482 767696 441139 567733 147776 306253 761445 715722 374230 516275 926328 836418 467170 598631 607546 424354 948673 112628 316373 708264 860404 012368 202151 992645 278388 782714 468428 403496 569904 318808 421998 407366 155874 114894 541689 730619 731603 694839 694769 536505 193434 739400 987718 607499 458402 677304 062560 143861 565638 281734 348254 387637 496717 818803 652522 882505 340546 755794 371628 696595 161026 845431 183009 013454 135470 755819 765831 377188 782290 959152 630001 019783 707618 809201 993129 761887 636556 789813 729589 525805 400562 792425 196513 939542 699017 850092 717447 316941 616801 960265 594715 447515 947305 971966 868050 035452 043999 548977 517451 182910 893248 163792 048318 735742 482714 841079 747703 467895 312737 601863 243064 808465 025145 898604 276662 636652 946387 116883 760035 642752 943615 203585 508594 777829 803493 167104 108381 517287 053671 744329 143503 747172 524695 457618 779708 640795 818829 407430 064061 479934 557954 605682 731483 763021 742583 974421 135188 034867 050176 979575 847566 706131 432789 240207 586393 046937 417168 202784 102823 356974 069323 056925 674887 881278 622734 637139 630769 488616 702830 422775 330578 848018 816334 302367 528611 202510 027856 412994 279734 350548 246521 457536 002460 471494 873650 742757 557359 968103 / 203 > 275585 [i]
- extracting embedded OOA [i] would yield OOA(275585, 2794, S27, 2, 5480), but