Best Known (58−29, 58, s)-Nets in Base 3
(58−29, 58, 37)-Net over F3 — Constructive and digital
Digital (29, 58, 37)-net over F3, using
- t-expansion [i] based on digital (27, 58, 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
(58−29, 58, 42)-Net over F3 — Digital
Digital (29, 58, 42)-net over F3, using
- net from sequence [i] based on digital (29, 41)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 29 and N(F) ≥ 42, using
(58−29, 58, 251)-Net in Base 3 — Upper bound on s
There is no (29, 58, 252)-net in base 3, because
- 1 times m-reduction [i] would yield (29, 57, 252)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 1601 352529 182744 843995 721513 > 357 [i]