Best Known (57−36, 57, s)-Nets in Base 9
(57−36, 57, 74)-Net over F9 — Constructive and digital
Digital (21, 57, 74)-net over F9, using
- t-expansion [i] based on digital (17, 57, 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
(57−36, 57, 88)-Net over F9 — Digital
Digital (21, 57, 88)-net over F9, using
- net from sequence [i] based on digital (21, 87)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 21 and N(F) ≥ 88, using
(57−36, 57, 981)-Net in Base 9 — Upper bound on s
There is no (21, 57, 982)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 2 466724 117829 736219 506402 387438 779782 971204 031695 343009 > 957 [i]