Best Known (30, 30+27, s)-Nets in Base 3
(30, 30+27, 37)-Net over F3 — Constructive and digital
Digital (30, 57, 37)-net over F3, using
- t-expansion [i] based on digital (27, 57, 37)-net over F3, using
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 26, N(F) = 36, and 1 place with degree 2 [i] based on function field F/F3 with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
(30, 30+27, 44)-Net over F3 — Digital
Digital (30, 57, 44)-net over F3, using
(30, 30+27, 309)-Net in Base 3 — Upper bound on s
There is no (30, 57, 310)-net in base 3, because
- 1 times m-reduction [i] would yield (30, 56, 310)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 532 729868 150153 808260 411061 > 356 [i]