Best Known (64, 85, s)-Nets in Base 25
(64, 85, 39064)-Net over F25 — Constructive and digital
Digital (64, 85, 39064)-net over F25, using
- 251 times duplication [i] based on digital (63, 84, 39064)-net over F25, using
- net defined by OOA [i] based on linear OOA(2584, 39064, F25, 21, 21) (dual of [(39064, 21), 820260, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2584, 390641, F25, 21) (dual of [390641, 390557, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2584, 390645, F25, 21) (dual of [390645, 390561, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(2581, 390626, F25, 21) (dual of [390626, 390545, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2565, 390626, F25, 17) (dual of [390626, 390561, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(253, 19, F25, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,25) or 19-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2584, 390645, F25, 21) (dual of [390645, 390561, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2584, 390641, F25, 21) (dual of [390641, 390557, 22]-code), using
- net defined by OOA [i] based on linear OOA(2584, 39064, F25, 21, 21) (dual of [(39064, 21), 820260, 22]-NRT-code), using
(64, 85, 390649)-Net over F25 — Digital
Digital (64, 85, 390649)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2585, 390649, F25, 21) (dual of [390649, 390564, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- linear OA(2581, 390625, F25, 21) (dual of [390625, 390544, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2561, 390625, F25, 16) (dual of [390625, 390564, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(254, 24, F25, 4) (dual of [24, 20, 5]-code or 24-arc in PG(3,25)), using
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- Reed–Solomon code RS(21,25) [i]
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
(64, 85, large)-Net in Base 25 — Upper bound on s
There is no (64, 85, large)-net in base 25, because
- 19 times m-reduction [i] would yield (64, 66, large)-net in base 25, but