Best Known (67−52, 67, s)-Nets in Base 25
(67−52, 67, 126)-Net over F25 — Constructive and digital
Digital (15, 67, 126)-net over F25, using
- t-expansion [i] based on digital (10, 67, 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
(67−52, 67, 140)-Net over F25 — Digital
Digital (15, 67, 140)-net over F25, using
- net from sequence [i] based on digital (15, 139)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 15 and N(F) ≥ 140, using
(67−52, 67, 1746)-Net in Base 25 — Upper bound on s
There is no (15, 67, 1747)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 4642 916857 674027 395817 934793 652685 023062 670858 916348 604422 870486 550984 472553 547485 477106 820049 > 2567 [i]