Best Known (10, 10+61, s)-Nets in Base 25
(10, 10+61, 126)-Net over F25 — Constructive and digital
Digital (10, 71, 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+61, 901)-Net in Base 25 — Upper bound on s
There is no (10, 71, 902)-net in base 25, because
- 1 times m-reduction [i] would yield (10, 70, 902)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 73 036602 575958 289677 401906 215888 839530 263904 522811 081811 879471 627400 697324 795732 884794 982436 299425 > 2570 [i]