Best Known (11, 74, s)-Nets in Base 25
(11, 74, 126)-Net over F25 — Constructive and digital
Digital (11, 74, 126)-net over F25, using
- t-expansion [i] based on digital (10, 74, 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
(11, 74, 997)-Net in Base 25 — Upper bound on s
There is no (11, 74, 998)-net in base 25, because
- 1 times m-reduction [i] would yield (11, 73, 998)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 1 152896 583093 040292 029099 686382 158133 491698 763485 114656 306010 634466 208580 058140 676976 587474 263094 387633 > 2573 [i]