Best Known (15, 15+91, s)-Nets in Base 27
(15, 15+91, 96)-Net over F27 — Constructive and digital
Digital (15, 106, 96)-net over F27, using
- t-expansion [i] based on digital (11, 106, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
(15, 15+91, 136)-Net over F27 — Digital
Digital (15, 106, 136)-net over F27, using
- t-expansion [i] based on digital (13, 106, 136)-net over F27, using
- net from sequence [i] based on digital (13, 135)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 13 and N(F) ≥ 136, using
- net from sequence [i] based on digital (13, 135)-sequence over F27, using
(15, 15+91, 1455)-Net over F27 — Upper bound on s (digital)
There is no digital (15, 106, 1456)-net over F27, because
- 1 times m-reduction [i] would yield digital (15, 105, 1456)-net over F27, but
- extracting embedded orthogonal array [i] would yield linear OA(27105, 1456, F27, 90) (dual of [1456, 1351, 91]-code), but
- the Johnson bound shows that N ≤ 58 372674 508112 224833 933851 934522 576132 156389 367308 387274 911661 400393 065075 623679 302362 636811 755189 757509 922570 970889 584671 170316 751578 212364 963776 110618 721667 127559 780285 510685 168170 182596 305286 113037 137731 277822 356577 302665 177840 396537 031178 963446 593360 182197 993692 494043 150021 481025 989079 206055 260051 128702 355782 694514 345502 318672 564474 145710 731717 830082 156585 101704 219752 177415 641008 651746 464592 679766 730436 007753 028897 522764 141436 078370 396796 056939 995435 072804 648649 563719 279658 861879 684755 734919 981991 645069 974112 616461 129746 925549 954356 830156 323723 957401 211251 546441 169123 562426 551517 869151 660084 813267 309308 551182 477905 615552 124701 059860 691428 498101 125481 472534 499574 414332 656149 737115 040664 407151 732407 907673 612486 561425 723225 885573 826464 139145 327924 185847 810885 323515 293761 114086 061454 591646 284177 073285 724452 524628 308019 235957 606137 487534 540555 320653 440550 589622 392233 349897 547794 153983 077615 469970 009052 138751 681327 583574 799150 722856 653858 293636 170486 334895 953796 070369 022741 117629 640192 416797 942921 792173 828766 317643 740360 041968 074136 645234 506536 499807 944827 906916 844897 511226 588425 916150 273946 964210 394544 141957 618106 594211 200957 188756 815320 777255 574532 924618 457190 127102 676237 761730 300293 245331 876864 568914 778075 545298 370998 643790 527267 479715 832525 618508 364651 340075 853503 399274 557517 705421 236182 743557 474898 362828 869193 822962 000655 948098 679404 338902 488649 663397 741746 354678 112377 206940 165129 386069 274785 733623 943704 424250 284267 695480 185747 916974 432189 501290 369668 581079 435271 616609 385980 147051 385915 728030 212866 197236 741015 346183 992085 987139 566675 833408 696455 262994 938937 807119 001118 208079 067337 102723 160838 431437 928653 430861 555410 284903 834948 640152 668109 235945 575197 226842 252138 658120 024634 908220 652074 445428 928150 918145 989747 169477 357777 605004 665652 724827 992986 310670 620090 071271 914653 262372 415492 249621 722410 842490 715209 601181 641289 743047 871329 804032 248680 752249 512672 262809 275934 341797 952427 555718 446133 663379 191093 < 271351 [i]
- extracting embedded orthogonal array [i] would yield linear OA(27105, 1456, F27, 90) (dual of [1456, 1351, 91]-code), but
(15, 15+91, 1459)-Net in Base 27 — Upper bound on s
There is no (15, 106, 1460)-net in base 27, because
- 1 times m-reduction [i] would yield (15, 105, 1460)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 2 022424 203608 503716 936443 170266 089108 048185 188711 040528 386028 462576 627071 682200 494355 235836 364095 359250 878283 141314 649665 522969 718751 793160 464671 744425 > 27105 [i]