Best Known (54−41, 54, s)-Nets in Base 25
(54−41, 54, 126)-Net over F25 — Constructive and digital
Digital (13, 54, 126)-net over F25, using
- t-expansion [i] based on digital (10, 54, 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
(54−41, 54, 1742)-Net in Base 25 — Upper bound on s
There is no (13, 54, 1743)-net in base 25, because
- 1 times m-reduction [i] would yield (13, 53, 1743)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 124 543142 065010 650192 923782 337622 609308 254144 649715 135891 437684 278770 358305 > 2553 [i]