Best Known (13, 13+43, s)-Nets in Base 25
(13, 13+43, 126)-Net over F25 — Constructive and digital
Digital (13, 56, 126)-net over F25, using
- t-expansion [i] based on digital (10, 56, 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+43, 1647)-Net in Base 25 — Upper bound on s
There is no (13, 56, 1648)-net in base 25, because
- 1 times m-reduction [i] would yield (13, 55, 1648)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 77998 854674 335547 741050 204616 711172 461870 167627 575320 286226 973218 040223 975553 > 2555 [i]