Best Known (50, 50+30, s)-Nets in Base 5
(50, 50+30, 252)-Net over F5 — Constructive and digital
Digital (50, 80, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 40, 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
(50, 50+30, 8570)-Net in Base 5 — Upper bound on s
There is no (50, 80, 8571)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 82 800777 220295 327930 203500 233466 040268 914598 176446 351861 > 580 [i]