Best Known (87−22, 87, s)-Nets in Base 25
(87−22, 87, 35512)-Net over F25 — Constructive and digital
Digital (65, 87, 35512)-net over F25, using
- 251 times duplication [i] based on digital (64, 86, 35512)-net over F25, using
- net defined by OOA [i] based on linear OOA(2586, 35512, F25, 22, 22) (dual of [(35512, 22), 781178, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2586, 390632, F25, 22) (dual of [390632, 390546, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2586, 390634, F25, 22) (dual of [390634, 390548, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(2585, 390625, F25, 22) (dual of [390625, 390540, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2577, 390625, F25, 20) (dual of [390625, 390548, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(251, 9, F25, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(2586, 390634, F25, 22) (dual of [390634, 390548, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(2586, 390632, F25, 22) (dual of [390632, 390546, 23]-code), using
- net defined by OOA [i] based on linear OOA(2586, 35512, F25, 22, 22) (dual of [(35512, 22), 781178, 23]-NRT-code), using
(87−22, 87, 354997)-Net over F25 — Digital
Digital (65, 87, 354997)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2587, 354997, F25, 22) (dual of [354997, 354910, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2587, 390639, F25, 22) (dual of [390639, 390552, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(2585, 390625, F25, 22) (dual of [390625, 390540, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2573, 390625, F25, 19) (dual of [390625, 390552, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(21) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(2587, 390639, F25, 22) (dual of [390639, 390552, 23]-code), using
(87−22, 87, large)-Net in Base 25 — Upper bound on s
There is no (65, 87, large)-net in base 25, because
- 20 times m-reduction [i] would yield (65, 67, large)-net in base 25, but