Best Known (48, 48+18, s)-Nets in Base 25
(48, 48+18, 1802)-Net over F25 — Constructive and digital
Digital (48, 66, 1802)-net over F25, using
- 251 times duplication [i] based on digital (47, 65, 1802)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (4, 13, 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 (34, 52, 1736)-net over F25, using
- net defined by OOA [i] based on linear OOA(2552, 1736, F25, 18, 18) (dual of [(1736, 18), 31196, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(2552, 15624, F25, 18) (dual of [15624, 15572, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2552, 15625, F25, 18) (dual of [15625, 15573, 19]-code), using
- an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(2552, 15625, F25, 18) (dual of [15625, 15573, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(2552, 15624, F25, 18) (dual of [15624, 15572, 19]-code), using
- net defined by OOA [i] based on linear OOA(2552, 1736, F25, 18, 18) (dual of [(1736, 18), 31196, 19]-NRT-code), using
- digital (4, 13, 66)-net over F25, using
- (u, u+v)-construction [i] based on
(48, 48+18, 79997)-Net over F25 — Digital
Digital (48, 66, 79997)-net over F25, using
(48, 48+18, large)-Net in Base 25 — Upper bound on s
There is no (48, 66, large)-net in base 25, because
- 16 times m-reduction [i] would yield (48, 50, large)-net in base 25, but