Best Known (64−53, 64, s)-Nets in Base 25
(64−53, 64, 126)-Net over F25 — Constructive and digital
Digital (11, 64, 126)-net over F25, using
- t-expansion [i] based on digital (10, 64, 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
(64−53, 64, 1058)-Net in Base 25 — Upper bound on s
There is no (11, 64, 1059)-net in base 25, because
- 1 times m-reduction [i] would yield (11, 63, 1059)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 11767 033515 094401 164171 373947 909569 980366 161759 982617 225037 621161 862646 992975 948682 437841 > 2563 [i]