Best Known (74−27, 74, s)-Nets in Base 5
(74−27, 74, 252)-Net over F5 — Constructive and digital
Digital (47, 74, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 37, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
(74−27, 74, 265)-Net over F5 — Digital
Digital (47, 74, 265)-net over F5, using
(74−27, 74, 11912)-Net in Base 5 — Upper bound on s
There is no (47, 74, 11913)-net in base 5, because
- 1 times m-reduction [i] would yield (47, 73, 11913)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 1059 632432 063945 307636 088323 757666 356928 401127 011765 > 573 [i]