Best Known (66−53, 66, s)-Nets in Base 25
(66−53, 66, 126)-Net over F25 — Constructive and digital
Digital (13, 66, 126)-net over F25, using
- t-expansion [i] based on digital (10, 66, 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
(66−53, 66, 1360)-Net in Base 25 — Upper bound on s
There is no (13, 66, 1361)-net in base 25, because
- 1 times m-reduction [i] would yield (13, 65, 1361)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 7 448508 556071 389918 978921 193178 317051 397002 098729 193328 842715 833642 170705 381787 080462 591665 > 2565 [i]