Best Known (11, 11+49, s)-Nets in Base 25
(11, 11+49, 126)-Net over F25 — Constructive and digital
Digital (11, 60, 126)-net over F25, using
- t-expansion [i] based on digital (10, 60, 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+49, 1103)-Net in Base 25 — Upper bound on s
There is no (11, 60, 1104)-net in base 25, because
- 1 times m-reduction [i] would yield (11, 59, 1104)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 30246 407161 910779 297994 448914 821530 229282 048821 213335 603358 819878 637220 462912 257025 > 2559 [i]