Best Known (69−58, 69, s)-Nets in Base 25
(69−58, 69, 126)-Net over F25 — Constructive and digital
Digital (11, 69, 126)-net over F25, using
- t-expansion [i] based on digital (10, 69, 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
(69−58, 69, 1015)-Net in Base 25 — Upper bound on s
There is no (11, 69, 1016)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 2 924232 224275 953467 992784 092016 174165 716968 562413 805525 435948 790071 852624 455337 987848 836172 969025 > 2569 [i]