Best Known (70, 193, s)-Nets in Base 3
(70, 193, 48)-Net over F3 — Constructive and digital
Digital (70, 193, 48)-net over F3, using
- t-expansion [i] based on digital (45, 193, 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
(70, 193, 82)-Net over F3 — Digital
Digital (70, 193, 82)-net over F3, using
- t-expansion [i] based on digital (69, 193, 82)-net over F3, using
- net from sequence [i] based on digital (69, 81)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 69 and N(F) ≥ 82, using
- net from sequence [i] based on digital (69, 81)-sequence over F3, using
(70, 193, 283)-Net over F3 — Upper bound on s (digital)
There is no digital (70, 193, 284)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(3193, 284, F3, 123) (dual of [284, 91, 124]-code), but
- residual code [i] would yield OA(370, 160, S3, 41), but
- the linear programming bound shows that M ≥ 237 414600 825052 605339 898199 161036 160905 519527 864586 535472 314868 452096 658656 264978 116155 882452 002220 053256 435156 976668 686347 726403 430562 706599 352511 621348 216092 041159 803048 965786 298333 323258 611041 118871 189616 553496 629315 483774 972599 246302 034772 157493 244417 809960 760744 207521 818016 988413 507021 348142 213336 494925 / 92442 752096 604942 178479 892415 842808 407405 887791 675287 977155 119754 877305 147007 945880 487028 463385 092034 013239 252418 811114 453981 675714 908592 981461 034409 612784 987754 955522 814374 638703 922669 543339 745948 692352 108779 197259 513447 911227 390404 751701 831689 423908 878212 005188 779482 752082 > 370 [i]
- residual code [i] would yield OA(370, 160, S3, 41), but
(70, 193, 292)-Net in Base 3 — Upper bound on s
There is no (70, 193, 293)-net in base 3, because
- 14 times m-reduction [i] would yield (70, 179, 293)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3179, 293, S3, 109), but
- 7 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]
- 7 times code embedding in larger space [i] would yield OA(3186, 300, S3, 109), but
- extracting embedded orthogonal array [i] would yield OA(3179, 293, S3, 109), but