Best Known (51−40, 51, s)-Nets in Base 25
(51−40, 51, 126)-Net over F25 — Constructive and digital
Digital (11, 51, 126)-net over F25, using
- t-expansion [i] based on digital (10, 51, 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
(51−40, 51, 1259)-Net in Base 25 — Upper bound on s
There is no (11, 51, 1260)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 197842 891814 520164 785062 568589 747783 512926 761771 434328 496441 989821 002625 > 2551 [i]