Best Known (58, 88, s)-Nets in Base 25
(58, 88, 1042)-Net over F25 — Constructive and digital
Digital (58, 88, 1042)-net over F25, using
- 1 times m-reduction [i] based on digital (58, 89, 1042)-net over F25, using
- net defined by OOA [i] based on linear OOA(2589, 1042, F25, 31, 31) (dual of [(1042, 31), 32213, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(2589, 15631, F25, 31) (dual of [15631, 15542, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2589, 15632, F25, 31) (dual of [15632, 15543, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- linear OA(2588, 15625, F25, 31) (dual of [15625, 15537, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2582, 15625, F25, 29) (dual of [15625, 15543, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(251, 7, F25, 1) (dual of [7, 6, 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(30) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(2589, 15632, F25, 31) (dual of [15632, 15543, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(2589, 15631, F25, 31) (dual of [15631, 15542, 32]-code), using
- net defined by OOA [i] based on linear OOA(2589, 1042, F25, 31, 31) (dual of [(1042, 31), 32213, 32]-NRT-code), using
(58, 88, 10371)-Net over F25 — Digital
Digital (58, 88, 10371)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2588, 10371, F25, 30) (dual of [10371, 10283, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2588, 15640, F25, 30) (dual of [15640, 15552, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(25) [i] based on
- linear OA(2585, 15625, F25, 30) (dual of [15625, 15540, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2573, 15625, F25, 26) (dual of [15625, 15552, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(253, 15, F25, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,25) or 15-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 Ce(29) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(2588, 15640, F25, 30) (dual of [15640, 15552, 31]-code), using
(58, 88, large)-Net in Base 25 — Upper bound on s
There is no (58, 88, large)-net in base 25, because
- 28 times m-reduction [i] would yield (58, 60, large)-net in base 25, but