Best Known (118−77, 118, s)-Nets in Base 3
(118−77, 118, 42)-Net over F3 — Constructive and digital
Digital (41, 118, 42)-net over F3, using
- t-expansion [i] based on digital (39, 118, 42)-net over F3, using
- net from sequence [i] based on digital (39, 41)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 39 and N(F) ≥ 42, using
- net from sequence [i] based on digital (39, 41)-sequence over F3, using
(118−77, 118, 56)-Net over F3 — Digital
Digital (41, 118, 56)-net over F3, using
- t-expansion [i] based on digital (40, 118, 56)-net over F3, using
- net from sequence [i] based on digital (40, 55)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 40 and N(F) ≥ 56, using
- net from sequence [i] based on digital (40, 55)-sequence over F3, using
(118−77, 118, 132)-Net in Base 3 — Upper bound on s
There is no (41, 118, 133)-net in base 3, because
- 2 times m-reduction [i] would yield (41, 116, 133)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3116, 133, S3, 75), but
- the linear programming bound shows that M ≥ 499 991160 796691 767829 311089 863604 958229 687121 227994 002589 482235 / 20 811757 > 3116 [i]
- extracting embedded orthogonal array [i] would yield OA(3116, 133, S3, 75), but