Best Known (13, 13+61, s)-Nets in Base 25
(13, 13+61, 126)-Net over F25 — Constructive and digital
Digital (13, 74, 126)-net over F25, using
- t-expansion [i] based on digital (10, 74, 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
(13, 13+61, 1249)-Net in Base 25 — Upper bound on s
There is no (13, 74, 1250)-net in base 25, because
- 1 times m-reduction [i] would yield (13, 73, 1250)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 1 128907 319467 982373 180159 311821 539632 154067 260975 924384 579818 609941 548707 686518 905153 564916 416938 207201 > 2573 [i]