Best Known (54−26, 54, s)-Nets in Base 3
(54−26, 54, 37)-Net over F3 — Constructive and digital
Digital (28, 54, 37)-net over F3, using
- t-expansion [i] based on digital (27, 54, 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
(54−26, 54, 40)-Net over F3 — Digital
Digital (28, 54, 40)-net over F3, using
(54−26, 54, 259)-Net in Base 3 — Upper bound on s
There is no (28, 54, 260)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 59 429627 240331 656676 879721 > 354 [i]