Best Known (11, 11+43, s)-Nets in Base 25
(11, 11+43, 126)-Net over F25 — Constructive and digital
Digital (11, 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
(11, 11+43, 1209)-Net in Base 25 — Upper bound on s
There is no (11, 54, 1210)-net in base 25, because
- 1 times m-reduction [i] would yield (11, 53, 1210)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 124 744021 154242 612959 276621 616968 621592 550321 614575 880357 872125 208309 722545 > 2553 [i]