Best Known (75−63, 75, s)-Nets in Base 25
(75−63, 75, 126)-Net over F25 — Constructive and digital
Digital (12, 75, 126)-net over F25, using
- t-expansion [i] based on digital (10, 75, 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
(75−63, 75, 1107)-Net in Base 25 — Upper bound on s
There is no (12, 75, 1108)-net in base 25, because
- 1 times m-reduction [i] would yield (12, 74, 1108)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 28 063148 737629 878125 000886 796631 224180 085609 860245 334174 399803 711115 101918 464931 685185 323359 386818 344097 > 2574 [i]