Best Known (76, 103, s)-Nets in Base 25
(76, 103, 30048)-Net over F25 — Constructive and digital
Digital (76, 103, 30048)-net over F25, using
- 252 times duplication [i] based on digital (74, 101, 30048)-net over F25, using
- net defined by OOA [i] based on linear OOA(25101, 30048, F25, 27, 27) (dual of [(30048, 27), 811195, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(25101, 390625, F25, 27) (dual of [390625, 390524, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- OOA 13-folding and stacking with additional row [i] based on linear OA(25101, 390625, F25, 27) (dual of [390625, 390524, 28]-code), using
- net defined by OOA [i] based on linear OOA(25101, 30048, F25, 27, 27) (dual of [(30048, 27), 811195, 28]-NRT-code), using
(76, 103, 214281)-Net over F25 — Digital
Digital (76, 103, 214281)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25103, 214281, F25, 27) (dual of [214281, 214178, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(25103, 390635, F25, 27) (dual of [390635, 390532, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(23) [i] based on
- linear OA(25101, 390625, F25, 27) (dual of [390625, 390524, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2593, 390625, F25, 24) (dual of [390625, 390532, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(252, 10, F25, 2) (dual of [10, 8, 3]-code or 10-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(26) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(25103, 390635, F25, 27) (dual of [390635, 390532, 28]-code), using
(76, 103, large)-Net in Base 25 — Upper bound on s
There is no (76, 103, large)-net in base 25, because
- 25 times m-reduction [i] would yield (76, 78, large)-net in base 25, but