Best Known (61−45, 61, s)-Nets in Base 25
(61−45, 61, 126)-Net over F25 — Constructive and digital
Digital (16, 61, 126)-net over F25, using
- t-expansion [i] based on digital (10, 61, 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
(61−45, 61, 150)-Net over F25 — Digital
Digital (16, 61, 150)-net over F25, using
- net from sequence [i] based on digital (16, 149)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 16 and N(F) ≥ 150, using
(61−45, 61, 2438)-Net in Base 25 — Upper bound on s
There is no (16, 61, 2439)-net in base 25, because
- 1 times m-reduction [i] would yield (16, 60, 2439)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 753548 872356 221393 454149 676906 616508 370643 286590 753026 429137 273725 416950 780782 767985 > 2560 [i]