Best Known (45−31, 45, s)-Nets in Base 5
(45−31, 45, 35)-Net over F5 — Constructive and digital
Digital (14, 45, 35)-net over F5, using
- net from sequence [i] based on digital (14, 34)-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 3 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]
(45−31, 45, 39)-Net over F5 — Digital
Digital (14, 45, 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
(45−31, 45, 169)-Net in Base 5 — Upper bound on s
There is no (14, 45, 170)-net in base 5, because
- 1 times m-reduction [i] would yield (14, 44, 170)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 5 786018 201215 409489 356046 528969 > 544 [i]