Best Known (31−19, 31, s)-Nets in Base 3
(31−19, 31, 20)-Net over F3 — Constructive and digital
Digital (12, 31, 20)-net over F3, using
- t-expansion [i] based on digital (11, 31, 20)-net over F3, using
- net from sequence [i] based on digital (11, 19)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 9, N(F) = 19, and 1 place with degree 3 [i] based on function field F/F3 with g(F) = 9 and N(F) ≥ 19, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (11, 19)-sequence over F3, using
(31−19, 31, 22)-Net over F3 — Digital
Digital (12, 31, 22)-net over F3, using
- net from sequence [i] based on digital (12, 21)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 12 and N(F) ≥ 22, using
(31−19, 31, 72)-Net in Base 3 — Upper bound on s
There is no (12, 31, 73)-net in base 3, because
- 1 times m-reduction [i] would yield (12, 30, 73)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 215 182443 828979 > 330 [i]