Best Known (10, 10+43, s)-Nets in Base 25
(10, 10+43, 126)-Net over F25 — Constructive and digital
Digital (10, 53, 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
(10, 10+43, 1035)-Net in Base 25 — Upper bound on s
There is no (10, 53, 1036)-net in base 25, because
- 1 times m-reduction [i] would yield (10, 52, 1036)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 4 939188 909917 672875 981729 283188 560978 068683 720023 060976 494134 653212 184225 > 2552 [i]