Best Known (184−119, 184, s)-Nets in Base 3
(184−119, 184, 48)-Net over F3 — Constructive and digital
Digital (65, 184, 48)-net over F3, using
- t-expansion [i] based on digital (45, 184, 48)-net over F3, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
(184−119, 184, 64)-Net over F3 — Digital
Digital (65, 184, 64)-net over F3, using
- t-expansion [i] based on digital (49, 184, 64)-net over F3, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 49 and N(F) ≥ 64, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
(184−119, 184, 252)-Net over F3 — Upper bound on s (digital)
There is no digital (65, 184, 253)-net over F3, because
- 2 times m-reduction [i] would yield digital (65, 182, 253)-net over F3, but
- extracting embedded orthogonal array [i] would yield linear OA(3182, 253, F3, 117) (dual of [253, 71, 118]-code), but
- residual code [i] would yield OA(365, 135, S3, 39), but
- the linear programming bound shows that M ≥ 2000 162801 965930 900770 104990 490349 087716 486277 017656 327637 447743 356893 611583 086779 033294 458144 297645 498065 069680 360497 586034 717055 695979 331533 067636 894184 274831 825929 542798 240773 136383 979404 789978 613217 511467 494994 164421 452551 885448 979128 358666 230809 782876 228996 614643 061101 386847 566758 402178 385246 751945 / 191 522914 058010 520813 141794 445584 294866 881432 434062 162321 677360 893054 150495 671472 738270 471466 591219 502187 129704 192350 637375 566977 609719 603428 016090 205950 883156 166286 858344 663375 557487 409407 465309 170228 124759 933260 238270 241796 215289 853172 624926 319292 770819 637055 510737 423757 > 365 [i]
- residual code [i] would yield OA(365, 135, S3, 39), but
- extracting embedded orthogonal array [i] would yield linear OA(3182, 253, F3, 117) (dual of [253, 71, 118]-code), but
(184−119, 184, 287)-Net in Base 3 — Upper bound on s
There is no (65, 184, 288)-net in base 3, because
- 10 times m-reduction [i] would yield (65, 174, 288)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3174, 288, S3, 109), but
- 12 times code embedding in larger space [i] would yield OA(3186, 300, S3, 109), but
- the linear programming bound shows that M ≥ 744 646766 850603 526568 601268 797422 932026 535817 992617 489413 629925 481692 835741 945421 210090 969950 381274 252816 504020 353660 158683 457200 925516 493661 440389 831805 338854 508258 811020 990136 433923 762970 235494 388055 889637 880458 633459 997426 817105 857222 614437 226587 / 10512 885684 310613 723066 595609 767913 116130 406095 478720 857818 594175 294259 025889 504412 156455 324830 169263 105843 888569 812652 562285 873819 443701 107860 316189 843301 339995 > 3186 [i]
- 12 times code embedding in larger space [i] would yield OA(3186, 300, S3, 109), but
- extracting embedded orthogonal array [i] would yield OA(3174, 288, S3, 109), but