Best Known (36−18, 36, s)-Nets in Base 25
(36−18, 36, 132)-Net over F25 — Constructive and digital
Digital (18, 36, 132)-net over F25, using
- 2 times m-reduction [i] based on digital (18, 38, 132)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (4, 14, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- digital (4, 24, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25 (see above)
- digital (4, 14, 66)-net over F25, using
- (u, u+v)-construction [i] based on
(36−18, 36, 317)-Net over F25 — Digital
Digital (18, 36, 317)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2536, 317, F25, 18) (dual of [317, 281, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2536, 624, F25, 18) (dual of [624, 588, 19]-code), using
(36−18, 36, 67495)-Net in Base 25 — Upper bound on s
There is no (18, 36, 67496)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 211 784322 742809 695475 678984 933475 782551 594452 822465 > 2536 [i]