Best Known (51−36, 51, s)-Nets in Base 5
(51−36, 51, 36)-Net over F5 — Constructive and digital
Digital (15, 51, 36)-net over F5, using
- net from sequence [i] based on digital (15, 35)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 11, N(F) = 32, and 4 places with degree 2 [i] based on function field F/F5 with g(F) = 11 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(51−36, 51, 39)-Net over F5 — Digital
Digital (15, 51, 39)-net over F5, using
- t-expansion [i] based on digital (14, 51, 39)-net over F5, using
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 14 and N(F) ≥ 39, using
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
(51−36, 51, 167)-Net in Base 5 — Upper bound on s
There is no (15, 51, 168)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 451616 439097 186003 989178 391572 397185 > 551 [i]