Best Known (80, 109, s)-Nets in Base 25
(80, 109, 27902)-Net over F25 — Constructive and digital
Digital (80, 109, 27902)-net over F25, using
- net defined by OOA [i] based on linear OOA(25109, 27902, F25, 29, 29) (dual of [(27902, 29), 809049, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(25109, 390629, F25, 29) (dual of [390629, 390520, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- linear OA(25109, 390625, F25, 29) (dual of [390625, 390516, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(25105, 390625, F25, 28) (dual of [390625, 390520, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(250, 4, F25, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- OOA 14-folding and stacking with additional row [i] based on linear OA(25109, 390629, F25, 29) (dual of [390629, 390520, 30]-code), using
(80, 109, 195314)-Net over F25 — Digital
Digital (80, 109, 195314)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25109, 195314, F25, 2, 29) (dual of [(195314, 2), 390519, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25109, 390628, F25, 29) (dual of [390628, 390519, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(25109, 390629, F25, 29) (dual of [390629, 390520, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- linear OA(25109, 390625, F25, 29) (dual of [390625, 390516, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(25105, 390625, F25, 28) (dual of [390625, 390520, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(250, 4, F25, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(25109, 390629, F25, 29) (dual of [390629, 390520, 30]-code), using
- OOA 2-folding [i] based on linear OA(25109, 390628, F25, 29) (dual of [390628, 390519, 30]-code), using
(80, 109, large)-Net in Base 25 — Upper bound on s
There is no (80, 109, large)-net in base 25, because
- 27 times m-reduction [i] would yield (80, 82, large)-net in base 25, but