Best Known (137−75, 137, s)-Nets in Base 9
(137−75, 137, 114)-Net over F9 — Constructive and digital
Digital (62, 137, 114)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (8, 45, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- digital (17, 92, 74)-net over F9, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- digital (8, 45, 40)-net over F9, using
(137−75, 137, 192)-Net over F9 — Digital
Digital (62, 137, 192)-net over F9, using
- t-expansion [i] based on digital (61, 137, 192)-net over F9, using
- net from sequence [i] based on digital (61, 191)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 61 and N(F) ≥ 192, using
- net from sequence [i] based on digital (61, 191)-sequence over F9, using
(137−75, 137, 5870)-Net in Base 9 — Upper bound on s
There is no (62, 137, 5871)-net in base 9, because
- 1 times m-reduction [i] would yield (62, 136, 5871)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 6021 095582 685653 377278 935610 756034 854280 187150 318639 530497 552412 145324 036520 806739 268054 571548 922890 347415 245000 337288 764603 226201 > 9136 [i]