Best Known (59, 59+31, s)-Nets in Base 25
(59, 59+31, 1042)-Net over F25 — Constructive and digital
Digital (59, 90, 1042)-net over F25, using
- 251 times duplication [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
(59, 59+31, 9473)-Net over F25 — Digital
Digital (59, 90, 9473)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2590, 9473, F25, 31) (dual of [9473, 9383, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2590, 15636, F25, 31) (dual of [15636, 15546, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(27) [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(2579, 15625, F25, 28) (dual of [15625, 15546, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(252, 11, F25, 2) (dual of [11, 9, 3]-code or 11-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(30) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(2590, 15636, F25, 31) (dual of [15636, 15546, 32]-code), using
(59, 59+31, large)-Net in Base 25 — Upper bound on s
There is no (59, 90, large)-net in base 25, because
- 29 times m-reduction [i] would yield (59, 61, large)-net in base 25, but