Best Known (66, 84, s)-Nets in Base 25
(66, 84, 43470)-Net over F25 — Constructive and digital
Digital (66, 84, 43470)-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 (53, 71, 43404)-net over F25, using
- net defined by OOA [i] based on linear OOA(2571, 43404, F25, 18, 18) (dual of [(43404, 18), 781201, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(2571, 390636, F25, 18) (dual of [390636, 390565, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2571, 390639, F25, 18) (dual of [390639, 390568, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(14) [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(2557, 390625, F25, 15) (dual of [390625, 390568, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(252, 14, F25, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- construction X applied to Ce(17) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(2571, 390639, F25, 18) (dual of [390639, 390568, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(2571, 390636, F25, 18) (dual of [390636, 390565, 19]-code), using
- net defined by OOA [i] based on linear OOA(2571, 43404, F25, 18, 18) (dual of [(43404, 18), 781201, 19]-NRT-code), using
- digital (4, 13, 66)-net over F25, using
(66, 84, 2416594)-Net over F25 — Digital
Digital (66, 84, 2416594)-net over F25, using
(66, 84, large)-Net in Base 25 — Upper bound on s
There is no (66, 84, large)-net in base 25, because
- 16 times m-reduction [i] would yield (66, 68, large)-net in base 25, but