Best Known (56−37, 56, s)-Nets in Base 5
(56−37, 56, 43)-Net over F5 — Constructive and digital
Digital (19, 56, 43)-net over F5, using
- t-expansion [i] based on digital (18, 56, 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
(56−37, 56, 45)-Net over F5 — Digital
Digital (19, 56, 45)-net over F5, using
- net from sequence [i] based on digital (19, 44)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 19 and N(F) ≥ 45, using
(56−37, 56, 245)-Net in Base 5 — Upper bound on s
There is no (19, 56, 246)-net in base 5, because
- 1 times m-reduction [i] would yield (19, 55, 246)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 290 502594 184799 671184 327291 556382 548865 > 555 [i]