Best Known (74, 74+54, s)-Nets in Base 5
(74, 74+54, 252)-Net over F5 — Constructive and digital
Digital (74, 128, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 64, 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, 74+54, 5603)-Net in Base 5 — Upper bound on s
There is no (74, 128, 5604)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 294637 022361 442022 738672 195246 625624 201388 232071 513385 247419 564194 910085 509920 041992 827793 > 5128 [i]