Best Known (12−9, 12, s)-Nets in Base 25
(12−9, 12, 52)-Net over F25 — Constructive and digital
Digital (3, 12, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
(12−9, 12, 56)-Net over F25 — Digital
Digital (3, 12, 56)-net over F25, using
- net from sequence [i] based on digital (3, 55)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 56, using
(12−9, 12, 642)-Net in Base 25 — Upper bound on s
There is no (3, 12, 643)-net in base 25, because
- 1 times m-reduction [i] would yield (3, 11, 643)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 2387 651212 329505 > 2511 [i]