Best Known (27, 27+31, s)-Nets in Base 3
(27, 27+31, 37)-Net over F3 — Constructive and digital
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]
(27, 27+31, 39)-Net over F3 — Digital
Digital (27, 58, 39)-net over F3, using
- net from sequence [i] based on digital (27, 38)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 27 and N(F) ≥ 39, using
(27, 27+31, 194)-Net in Base 3 — Upper bound on s
There is no (27, 58, 195)-net in base 3, because
- 1 times m-reduction [i] would yield (27, 57, 195)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 1599 765539 704369 664327 707635 > 357 [i]