Best Known (58−37, 58, s)-Nets in Base 5
(58−37, 58, 43)-Net over F5 — Constructive and digital
Digital (21, 58, 43)-net over F5, using
- t-expansion [i] based on digital (18, 58, 43)-net over F5, using
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 17, N(F) = 42, and 1 place with degree 2 [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
(58−37, 58, 50)-Net over F5 — Digital
Digital (21, 58, 50)-net over F5, using
- net from sequence [i] based on digital (21, 49)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 21 and N(F) ≥ 50, using
(58−37, 58, 295)-Net in Base 5 — Upper bound on s
There is no (21, 58, 296)-net in base 5, because
- 1 times m-reduction [i] would yield (21, 57, 296)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 6999 518931 522830 241693 239259 092454 900865 > 557 [i]