Best Known (82, ∞, s)-Nets in Base 27
(82, ∞, 324)-Net over F27 — Constructive and digital
Digital (82, m, 324)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (82, 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
(82, ∞, 325)-Net over F27 — Digital
Digital (82, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (82, 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
(82, ∞, 2192)-Net in Base 27 — Upper bound on s
There is no (82, m, 2193)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (82, 4383, 2193)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(274383, 2193, S27, 2, 4301), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 171598 615033 245767 972105 599323 954208 511685 444722 668539 693786 603777 130457 139982 216057 938393 221009 121767 974416 803048 331789 234680 505926 229211 738455 910143 728808 384212 089437 947376 215541 032802 495303 079466 013837 373879 959902 047248 246836 081124 632784 484961 764653 500833 176610 500483 020813 149895 243808 844159 518560 106853 862049 450964 163711 487649 232423 135145 566972 860505 867470 547829 431881 919105 584454 954270 974638 086969 748737 191748 761113 512659 861473 676507 742345 085892 063695 234940 376032 112771 947414 232957 494912 027510 392172 908672 978825 081250 619346 901363 966812 902156 142444 482274 430250 147121 001306 125743 992990 313249 387792 460301 636615 297294 029734 996396 010148 762210 292971 828314 012339 540229 177718 291370 878293 562091 037117 572655 274518 046757 458090 139354 708589 164314 455677 190652 146420 345282 843237 034152 741467 766161 553576 394913 086444 315569 354957 718370 423812 984674 055512 692412 503339 575111 619684 020002 318739 477153 002420 236552 987112 396865 040224 771391 372725 857265 944520 198224 548985 975055 579799 163537 884001 996759 520814 733813 645239 474019 676966 424162 186103 872787 569119 925362 674913 539330 346161 771688 749518 086519 363751 969408 726240 325985 690511 134259 749861 033263 664656 837207 687743 650945 068797 388327 971709 881403 541442 749147 535863 728387 949553 031718 267308 755264 473021 606265 142102 428254 942220 225217 606039 198297 385410 092167 542381 251708 268388 693774 507827 888518 963655 615263 339781 842761 643033 642827 722380 728979 094299 556414 553786 582996 590910 652427 584410 675064 603660 046142 506213 152212 902054 785641 939975 960572 530851 208673 533852 477106 485816 114900 414802 836442 494206 893989 690584 166660 026926 749073 538795 610465 210699 208878 479004 397040 648124 664808 732581 409822 331622 490382 242786 695007 179009 252598 120515 870237 636702 823231 005891 523171 242414 042873 074553 351412 169914 495049 870817 836026 380326 508160 566586 093007 408342 478683 703944 390141 189015 509256 139395 160539 319325 783311 977233 664220 434248 437019 958501 779448 007744 155679 011982 735605 942910 153429 950905 588213 673402 721159 201794 191133 596821 897773 013156 696468 542009 953878 129618 468557 062660 054813 415563 083781 155125 985029 132738 455754 027184 906850 244307 459183 755640 684476 735830 012652 362290 465490 560229 210208 828267 491256 289330 704101 204860 432319 474223 775288 674513 742791 579903 873108 824360 557327 109813 098778 249686 585517 392800 305257 203826 255519 253393 910720 343160 861597 418121 864928 884110 033979 888698 624041 441872 175157 847689 993217 022371 771199 838546 420036 345927 865452 464826 431001 011795 761197 868887 896005 113001 319898 875125 975064 169995 735841 091738 821619 290775 914263 883486 053777 362773 858436 917352 718195 197137 607310 165687 808735 659532 815899 103988 093979 737967 199776 867630 851138 865980 146978 048219 924891 126625 807455 740317 554058 488370 354158 516516 200509 290834 133700 892881 421761 658106 293608 306649 164765 222421 199281 014688 988002 401228 609642 683592 589388 605815 169736 038732 801920 117099 994151 808731 301233 270505 461985 351573 306521 146306 207152 758272 854784 051513 311114 381472 757007 746966 822824 672592 496073 325225 597637 513406 748647 751842 922313 871766 631000 031263 489590 833978 377205 336437 842186 841996 677075 776872 300415 334517 045484 717787 702601 878296 796923 502514 524023 206343 738671 234453 414321 636038 342847 082820 086350 080922 197688 636283 725525 223557 906532 906867 618297 364189 632101 914819 593188 856527 382986 907614 191006 058222 270588 451481 348747 956861 528077 665898 209626 459567 694262 475815 982551 489150 210576 310079 992438 392162 320353 400418 361529 679174 913754 794291 034487 124387 933095 712696 331276 703320 552880 222036 654301 872445 589550 916157 471312 570361 554265 844088 008717 858633 102840 005122 613242 824828 754982 092613 973564 304525 534103 296339 705188 253918 207835 754591 781223 952462 679695 376802 745207 360220 871591 163188 189404 053623 321777 330344 359248 703010 668627 051659 694042 941649 743417 888473 003141 404239 730204 145558 187627 541920 810631 590554 171563 497079 469033 711206 848855 942594 720985 148729 428908 583997 884623 377284 268897 691110 854247 771562 117221 385935 835534 688483 551274 019452 302684 380780 298839 382091 364352 162821 026464 932714 574807 531841 367530 354671 846652 028611 055624 410394 607858 315508 831210 300824 571568 294582 003697 731190 063986 694273 204152 123555 628803 213227 001766 246494 725053 739986 548993 071188 897963 726534 988058 187455 954291 677328 965478 461068 645091 955521 658359 877956 787183 307065 909350 712614 056465 469392 923354 325341 312261 505836 256409 681783 344260 601393 155214 857030 975758 888093 729250 592458 821778 738453 002111 703482 790251 513964 437528 096765 404204 191130 022422 029314 321955 225759 716264 936191 113489 173790 623818 903431 974757 023307 538099 154616 925336 389748 192783 584765 836502 568021 103157 862078 252892 228332 474106 576848 016041 108416 634549 235699 841243 528020 275981 141254 867015 757236 463312 911623 119863 510898 525492 267609 021711 182997 030433 300302 175086 589538 679509 010345 314553 004028 749984 547018 942378 254724 742600 991344 280948 538665 421225 345234 243363 128291 822664 954737 181869 626533 001989 668681 397093 946190 743153 632597 919416 522369 939704 510492 940194 057769 338161 413958 000738 437142 971809 172467 039483 548953 649082 915693 691803 944741 786571 886001 805085 061644 401107 535921 248501 125999 233825 508470 107538 715161 644217 049982 972334 761979 730899 620738 410531 439674 975984 820858 675829 443389 662498 919814 817773 603128 010571 681717 589064 144112 961398 989824 872166 672370 860143 151043 946527 957627 695699 141002 746470 434203 405355 593471 340107 940500 746999 973739 068211 241555 435434 898142 494189 061928 682871 229364 215478 857251 911988 325022 267160 632505 588863 446913 372196 374841 185195 467616 583643 582322 026704 004536 706838 059478 101715 915433 878318 517975 418025 521072 948808 458909 882127 516051 901135 985724 791630 846604 793183 791792 097911 943326 200302 707012 664260 612538 358262 447349 141525 098325 388230 391754 368882 261066 151035 840421 823325 760299 401207 532027 704492 431465 398289 160201 739991 447465 699378 138852 369235 687476 422199 290938 862268 634139 202236 520396 013064 374841 133557 253370 017103 827967 141464 619814 154743 800400 341581 565399 323934 793833 699866 767320 810543 615287 428520 196206 800586 502358 680012 488939 628094 175568 510712 325747 905266 009393 928120 238735 050135 372368 709061 536956 690582 923036 808183 053458 469126 079347 272361 311701 669508 248192 692293 188769 701151 558957 080339 172877 713679 504969 608980 751094 782277 920064 774712 972813 521312 302963 786131 388257 941307 661745 411283 579906 735789 757453 768797 980136 992239 528343 120848 531219 925365 288480 791479 766882 990450 922407 180201 918753 894640 406167 774333 079975 856638 954914 831442 687789 705732 417370 437001 863660 066468 053994 303669 820150 749735 439751 162905 228533 191095 542445 730541 712998 369111 342385 517799 901364 299361 191264 734857 856043 305226 612916 / 239 > 274383 [i]
- extracting embedded OOA [i] would yield OOA(274383, 2193, S27, 2, 4301), but