Best Known (140−90, 140, s)-Nets in Base 3
(140−90, 140, 48)-Net over F3 — Constructive and digital
Digital (50, 140, 48)-net over F3, using
- t-expansion [i] based on digital (45, 140, 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
(140−90, 140, 64)-Net over F3 — Digital
Digital (50, 140, 64)-net over F3, using
- t-expansion [i] based on digital (49, 140, 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
(140−90, 140, 203)-Net over F3 — Upper bound on s (digital)
There is no digital (50, 140, 204)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(3140, 204, F3, 90) (dual of [204, 64, 91]-code), but
- residual code [i] would yield OA(350, 113, S3, 30), but
- the linear programming bound shows that M ≥ 596 570195 583823 721692 911689 409545 159333 416347 007509 353942 840802 048696 218909 803001 021000 425338 904291 291412 200954 459797 559193 112998 126796 056497 666716 210000 / 790 509540 724661 767547 670804 913087 923304 064947 691066 061183 661201 682713 479390 203130 739891 928552 692939 503065 752658 282066 469332 139629 > 350 [i]
- residual code [i] would yield OA(350, 113, S3, 30), but
(140−90, 140, 227)-Net in Base 3 — Upper bound on s
There is no (50, 140, 228)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 7 198114 551530 622878 215844 339916 313619 524692 605821 929620 217916 222761 > 3140 [i]