Best Known (90−72, 90, s)-Nets in Base 25
(90−72, 90, 126)-Net over F25 — Constructive and digital
Digital (18, 90, 126)-net over F25, using
- t-expansion [i] based on digital (10, 90, 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
(90−72, 90, 153)-Net over F25 — Digital
Digital (18, 90, 153)-net over F25, using
- net from sequence [i] based on digital (18, 152)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 18 and N(F) ≥ 153, using
(90−72, 90, 1840)-Net in Base 25 — Upper bound on s
There is no (18, 90, 1841)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 659430 332192 389887 275683 008855 437860 637815 206148 752917 805439 350453 534742 575558 885365 776674 248753 333506 212218 512673 320324 702945 > 2590 [i]