Best Known (42, 118, s)-Nets in Base 3
(42, 118, 42)-Net over F3 — Constructive and digital
Digital (42, 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
(42, 118, 56)-Net over F3 — Digital
Digital (42, 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
(42, 118, 136)-Net in Base 3 — Upper bound on s
There is no (42, 118, 137)-net in base 3, because
- 1 times m-reduction [i] would yield (42, 117, 137)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3117, 137, S3, 75), but
- the linear programming bound shows that M ≥ 2 512290 520419 287793 177886 934344 555139 842858 289208 378001 236620 873421 / 34498 790200 > 3117 [i]
- extracting embedded orthogonal array [i] would yield OA(3117, 137, S3, 75), but