Best Known (54−36, 54, s)-Nets in Base 25
(54−36, 54, 126)-Net over F25 — Constructive and digital
Digital (18, 54, 126)-net over F25, using
- t-expansion [i] based on digital (10, 54, 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
(54−36, 54, 153)-Net over F25 — Digital
Digital (18, 54, 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
(54−36, 54, 4908)-Net in Base 25 — Upper bound on s
There is no (18, 54, 4909)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 3090 620271 704109 968606 263251 019020 550042 739813 948683 701129 971797 491812 935345 > 2554 [i]