Best Known (82−18, 82, s)-Nets in Base 25
(82−18, 82, 43469)-Net over F25 — Constructive and digital
Digital (64, 82, 43469)-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 (51, 69, 43403)-net over F25, using
- net defined by OOA [i] based on linear OOA(2569, 43403, F25, 18, 18) (dual of [(43403, 18), 781185, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(2569, 390627, F25, 18) (dual of [390627, 390558, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2569, 390629, F25, 18) (dual of [390629, 390560, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(2569, 390625, F25, 18) (dual of [390625, 390556, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2565, 390625, F25, 17) (dual of [390625, 390560, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(250, 4, F25, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(2569, 390629, F25, 18) (dual of [390629, 390560, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(2569, 390627, F25, 18) (dual of [390627, 390558, 19]-code), using
- net defined by OOA [i] based on linear OOA(2569, 43403, F25, 18, 18) (dual of [(43403, 18), 781185, 19]-NRT-code), using
- digital (4, 13, 66)-net over F25, using
(82−18, 82, 1654783)-Net over F25 — Digital
Digital (64, 82, 1654783)-net over F25, using
(82−18, 82, large)-Net in Base 25 — Upper bound on s
There is no (64, 82, large)-net in base 25, because
- 16 times m-reduction [i] would yield (64, 66, large)-net in base 25, but