Best Known (112−61, 112, s)-Nets in Base 9
(112−61, 112, 104)-Net over F9 — Constructive and digital
Digital (51, 112, 104)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (8, 38, 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 (13, 74, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- digital (8, 38, 40)-net over F9, using
(112−61, 112, 182)-Net over F9 — Digital
Digital (51, 112, 182)-net over F9, using
- t-expansion [i] based on digital (50, 112, 182)-net over F9, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 50 and N(F) ≥ 182, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
(112−61, 112, 5091)-Net in Base 9 — Upper bound on s
There is no (51, 112, 5092)-net in base 9, because
- 1 times m-reduction [i] would yield (51, 111, 5092)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 8360 934159 750063 886264 539064 532766 252341 391256 239903 710853 514555 758500 154405 635503 058496 692817 478044 879169 > 9111 [i]