Best Known (11, 11+27, s)-Nets in Base 25
(11, 11+27, 126)-Net over F25 — Constructive and digital
Digital (11, 38, 126)-net over F25, using
- t-expansion [i] based on digital (10, 38, 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
(11, 11+27, 2242)-Net in Base 25 — Upper bound on s
There is no (11, 38, 2243)-net in base 25, because
- 1 times m-reduction [i] would yield (11, 37, 2243)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 5317 123991 231720 055371 702840 931208 906610 752963 416745 > 2537 [i]