Best Known (40−25, 40, s)-Nets in Base 5
(40−25, 40, 36)-Net over F5 — Constructive and digital
Digital (15, 40, 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]
(40−25, 40, 39)-Net over F5 — Digital
Digital (15, 40, 39)-net over F5, using
- t-expansion [i] based on digital (14, 40, 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
(40−25, 40, 238)-Net in Base 5 — Upper bound on s
There is no (15, 40, 239)-net in base 5, because
- 1 times m-reduction [i] would yield (15, 39, 239)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 1841 012671 764347 014866 659793 > 539 [i]