Best Known (86−22, 86, s)-Nets in Base 25
(86−22, 86, 35512)-Net over F25 — Constructive and digital
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
(86−22, 86, 302222)-Net over F25 — Digital
Digital (64, 86, 302222)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2586, 302222, F25, 22) (dual of [302222, 302136, 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
(86−22, 86, large)-Net in Base 25 — Upper bound on s
There is no (64, 86, large)-net in base 25, because
- 20 times m-reduction [i] would yield (64, 66, large)-net in base 25, but