Best Known (13, 13+51, s)-Nets in Base 25
(13, 13+51, 126)-Net over F25 — Constructive and digital
Digital (13, 64, 126)-net over F25, using
- t-expansion [i] based on digital (10, 64, 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+51, 1400)-Net in Base 25 — Upper bound on s
There is no (13, 64, 1401)-net in base 25, because
- 1 times m-reduction [i] would yield (13, 63, 1401)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 11911 845577 107120 750158 025053 118948 671022 637325 793915 669001 955884 491390 414928 944263 420569 > 2563 [i]