Best Known (47−31, 47, s)-Nets in Base 5
(47−31, 47, 37)-Net over F5 — Constructive and digital
Digital (16, 47, 37)-net over F5, using
- net from sequence [i] based on digital (16, 36)-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 5 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]
(47−31, 47, 40)-Net over F5 — Digital
Digital (16, 47, 40)-net over F5, using
- net from sequence [i] based on digital (16, 39)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 16 and N(F) ≥ 40, using
(47−31, 47, 212)-Net in Base 5 — Upper bound on s
There is no (16, 47, 213)-net in base 5, because
- 1 times m-reduction [i] would yield (16, 46, 213)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 143 045571 723442 647592 504828 482845 > 546 [i]