Best Known (69−54, 69, s)-Nets in Base 25
(69−54, 69, 126)-Net over F25 — Constructive and digital
Digital (15, 69, 126)-net over F25, using
- t-expansion [i] based on digital (10, 69, 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
(69−54, 69, 140)-Net over F25 — Digital
Digital (15, 69, 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
(69−54, 69, 1686)-Net in Base 25 — Upper bound on s
There is no (15, 69, 1687)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 2 873522 118145 097133 948442 460880 656731 834454 968227 487700 821243 013682 576874 892738 905138 641491 147065 > 2569 [i]