Best Known (99, ∞, s)-Nets in Base 27
(99, ∞, 324)-Net over F27 — Constructive and digital
Digital (99, m, 324)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (99, 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
(99, ∞, 325)-Net over F27 — Digital
Digital (99, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (99, 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
(99, ∞, 2636)-Net in Base 27 — Upper bound on s
There is no (99, m, 2637)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (99, 5271, 2637)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(275271, 2637, S27, 2, 5172), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 922368 591769 727141 779235 163762 798023 089706 433814 640467 814483 449138 421335 968947 944914 922608 759731 233581 166199 974957 918444 281244 463397 290302 938696 069740 208508 919863 248765 089915 582765 335604 353843 154927 045413 420661 429008 006118 632765 953543 218702 007977 734590 435166 315939 460848 145208 235409 031369 357391 848318 081284 780274 321450 001213 302609 724899 410261 393257 985345 484092 824930 173085 810702 451099 078773 672598 079227 470402 411047 363509 442175 741323 907022 103428 230523 800032 393896 347144 828538 808811 774685 681173 863035 945549 057823 048583 517781 226714 899449 472475 547307 951996 020316 880580 117325 460256 521816 274649 160608 639793 933622 133185 522658 229345 933997 038166 774944 170944 739927 395732 827125 551017 714617 125467 427757 399837 710205 162647 834894 643590 317935 554823 031284 457278 117052 408470 281085 675531 607661 881574 246594 114010 999255 968096 447170 091240 185672 818723 288218 608193 516935 806228 946920 664143 215148 276374 939154 232298 204923 608551 814868 593586 937174 309534 805863 440117 644937 489113 170725 267372 394863 574889 485696 329935 693784 748926 699725 063078 039162 974498 284702 699746 425595 893773 740638 341213 403228 105049 663950 672857 969271 054444 649270 387879 170231 930496 298974 042079 981933 545930 524044 915731 139697 761215 889793 166114 117811 782813 438964 555210 078145 277441 842966 052924 077487 341560 318527 472614 380308 314699 020163 282928 291610 035134 731409 209804 696059 676612 776402 347379 288415 493904 732824 038017 265872 391341 561633 155169 018767 349214 910256 172535 241090 775867 255388 981251 288959 321480 619816 564480 381074 574077 121835 486205 223010 322251 250069 234551 933636 667156 861618 654589 656031 314140 972720 049188 272224 644790 225148 552751 677615 196927 680787 327113 635287 495410 837765 029302 383274 859653 589452 960440 096015 900662 142318 535152 856649 504528 823602 818013 747093 370067 340275 527776 684403 545487 661599 055332 874929 696101 706734 658256 392615 490298 694779 402131 803427 106917 759947 703126 655193 353071 819712 932884 529109 232873 934609 675090 719648 797048 209393 576735 550486 836392 194577 906903 935788 522523 292421 650791 008615 623042 796819 809837 884228 019620 234867 784159 381298 313240 130457 550805 810233 790651 257100 898866 762491 208472 636438 448367 670872 128116 647663 625751 886374 446949 378163 016127 311899 142269 304645 575731 068081 265304 768360 914870 734068 843762 984746 315438 724275 513670 712881 416471 005019 183412 837169 903338 348758 418819 211011 479494 106349 478592 799775 678079 118502 312023 250089 842826 172284 945860 605066 280840 366886 658634 612320 531131 195411 611253 953085 416905 949807 406558 647781 860366 331536 779186 871964 732131 380599 317574 951506 713341 753278 271074 082501 092656 871396 323185 557567 420120 784115 133901 180079 886391 367729 997229 925452 028904 239885 979985 329574 462237 175398 904781 527764 748794 952327 545820 583297 066671 437822 547233 781508 122705 957448 876562 420181 576669 491072 185426 084876 892987 450623 904781 413672 646851 457213 889546 506106 601815 636163 853578 434938 613232 849580 838509 203689 374817 093240 987650 314694 194891 195090 173142 869629 093096 499234 764000 406634 964246 286673 509596 338492 985017 565576 468392 972299 443845 447011 368721 571430 152607 480323 223180 924073 915998 662053 293954 824429 219127 347307 721323 609814 314092 699752 562176 932168 160731 274502 383359 025345 822730 233050 347361 804398 878732 232154 747720 396044 644399 066279 648509 309551 018988 345066 747985 372872 178216 037214 566826 476621 364560 044010 039332 949222 389261 414997 576728 329711 719022 513364 986979 976880 424129 839654 801834 434492 362602 092482 103849 662576 460331 769643 906265 615847 312766 453581 544566 882505 220707 431703 951593 336872 296200 467417 358406 350687 755000 668124 046331 256138 445029 774069 147738 390637 823717 136941 655356 031185 546359 093944 079185 953218 563358 943756 269146 625971 666731 037504 988439 139266 520348 577490 933387 161581 863014 690036 538585 406847 351227 203334 544627 344016 735687 214139 325980 294309 387496 723443 745156 904460 110751 355192 120277 081368 433937 065254 623620 232425 637763 563211 278332 377486 065879 109833 938155 723586 332512 077055 065100 681089 880954 008336 460343 629765 213167 934859 141918 290251 348304 620995 102916 428849 259362 650044 152108 162663 462312 372276 334533 192455 048545 026450 657250 264547 715142 405683 129854 199323 126334 385074 129140 419786 987414 612380 976585 820840 429325 882627 813125 237569 507662 563817 356086 785855 567607 814734 845822 946410 330679 723222 604473 026743 609921 441657 602387 974476 569177 081178 498189 509548 795237 473283 794832 983443 491191 941593 087852 660239 282415 748659 692166 776963 367390 119233 402618 809384 311089 857786 276234 336732 419334 745251 353934 492416 188740 044107 448934 901555 783849 551148 038665 094574 041875 816707 904331 100354 128974 931404 990380 076257 580321 102772 811125 866937 398984 799878 649541 058422 918188 512941 296825 417597 535789 812784 366789 978365 463892 349714 200743 905517 885529 960106 500376 437703 992993 444901 107287 634349 496296 011154 145279 552394 398386 778167 201460 837391 994446 508480 139909 408544 158331 037883 170041 270431 527102 874719 358134 709772 282353 476798 458060 671303 086382 526775 156171 415358 887178 852624 327394 126338 517915 355660 674116 037906 410410 055335 654285 336094 312869 565345 651902 390215 359755 262565 336268 309303 569900 540614 418243 140146 884527 074130 969868 294172 212271 382308 277837 593129 188748 210896 435091 471411 903243 012477 719472 230866 348465 061569 716400 724541 007835 881288 141090 799909 396831 963792 479167 450398 527105 220492 105149 948360 093816 295212 285516 609123 600720 109417 675494 293044 957589 359212 244892 313742 809581 831839 048494 903823 988181 505928 151151 066313 106114 134030 922250 228247 515779 137942 922266 799434 374083 295368 990030 101298 303453 771569 028724 605049 404020 396493 035984 502609 074417 290443 325695 249207 513059 009925 300731 153902 563388 802140 997166 354542 946448 931198 739699 228653 247889 296366 399531 946365 461419 761225 417098 385285 184943 420614 063200 855279 500489 352538 548465 240395 614675 934544 894230 800439 689121 337282 022982 840258 160067 248815 757374 327022 988446 740477 782944 045024 650707 398026 557992 816325 576503 782769 287706 984676 270637 808200 098739 287719 527747 058720 073264 003970 110590 830885 566475 184562 729584 777134 778556 912520 997489 484446 632200 373009 794163 678576 211879 633270 571872 832640 926372 387977 090776 846507 526577 697989 614105 894283 581208 350854 010396 796427 465525 342201 173103 670951 381142 386523 969317 915310 061872 624417 208485 304879 481561 990827 032923 212453 979685 721278 302339 959205 745795 564295 917732 907599 621470 082289 527578 442738 758176 864784 364369 343895 209045 570315 135416 025667 679596 564946 147243 136735 311715 739165 920933 066529 475566 862336 210730 741252 421405 496142 104850 395586 331321 859998 132499 502927 742448 719708 497579 487638 853368 292240 313677 381062 395713 167012 617773 123198 629574 116609 361370 676415 718489 266422 029936 889661 105163 523324 787071 424523 636280 706842 688399 272818 555944 542030 001494 830527 745333 487319 025581 594132 094841 714275 281972 951423 781137 929152 174425 642374 906671 722402 801803 878874 443450 878515 315315 901167 401248 944752 887317 464370 813427 789517 562475 333213 164956 856755 684675 975226 586235 192678 708624 464740 979565 956205 993600 096467 474638 868677 577838 838506 155759 929063 368157 859996 238911 664715 127026 990586 397264 817412 278966 483733 822482 773547 519305 016975 544108 098581 110320 022286 590287 813531 002509 878860 817750 226254 062060 580192 575254 628324 509940 785043 450477 982101 033174 137102 585762 529698 441131 659429 772018 599547 074587 995122 637518 309039 164819 916467 660337 255118 632479 858836 275527 908983 179023 543643 237353 090239 773332 902472 946873 810692 986328 365783 837256 608388 560092 407628 649401 386257 280628 797957 559732 324296 838791 050581 659220 038444 504473 319099 411270 553908 815722 443148 571973 656696 853582 643904 423882 468551 622769 972585 579237 930315 101411 090499 102853 846043 287827 980120 878491 728300 721986 936293 738130 329324 775034 856778 634477 453620 720579 302722 829262 521172 382446 204577 160965 560379 649134 606030 419543 858474 438686 218851 202506 455960 011604 641267 141126 798356 116668 291212 656420 582232 385848 004976 303182 965834 651918 119852 878907 085923 384959 038201 258380 183332 047730 943925 974213 452789 903010 038173 969204 807315 252223 246304 243247 / 5173 > 275271 [i]
- extracting embedded OOA [i] would yield OOA(275271, 2637, S27, 2, 5172), but