Best Known (42−24, 42, s)-Nets in Base 25
(42−24, 42, 126)-Net over F25 — Constructive and digital
Digital (18, 42, 126)-net over F25, using
- t-expansion [i] based on digital (10, 42, 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
(42−24, 42, 153)-Net over F25 — Digital
Digital (18, 42, 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
(42−24, 42, 17210)-Net in Base 25 — Upper bound on s
There is no (18, 42, 17211)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 51723 455948 536982 815130 329001 320025 357719 562168 244972 765025 > 2542 [i]