Best Known (87−29, 87, s)-Nets in Base 25
(87−29, 87, 1117)-Net over F25 — Constructive and digital
Digital (58, 87, 1117)-net over F25, using
- 251 times duplication [i] based on digital (57, 86, 1117)-net over F25, using
- net defined by OOA [i] based on linear OOA(2586, 1117, F25, 29, 29) (dual of [(1117, 29), 32307, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2586, 15639, F25, 29) (dual of [15639, 15553, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2586, 15641, F25, 29) (dual of [15641, 15555, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(23) [i] based on
- 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(2570, 15625, F25, 24) (dual of [15625, 15555, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(254, 16, F25, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,25)), using
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- Reed–Solomon code RS(21,25) [i]
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- construction X applied to Ce(28) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(2586, 15641, F25, 29) (dual of [15641, 15555, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2586, 15639, F25, 29) (dual of [15639, 15553, 30]-code), using
- net defined by OOA [i] based on linear OOA(2586, 1117, F25, 29, 29) (dual of [(1117, 29), 32307, 30]-NRT-code), using
(87−29, 87, 12895)-Net over F25 — Digital
Digital (58, 87, 12895)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2587, 12895, F25, 29) (dual of [12895, 12808, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2587, 15645, F25, 29) (dual of [15645, 15558, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(22) [i] based on
- 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(2567, 15625, F25, 23) (dual of [15625, 15558, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(255, 20, F25, 5) (dual of [20, 15, 6]-code or 20-arc in PG(4,25)), using
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
- Reed–Solomon code RS(20,25) [i]
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
- construction X applied to Ce(28) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(2587, 15645, F25, 29) (dual of [15645, 15558, 30]-code), using
(87−29, 87, large)-Net in Base 25 — Upper bound on s
There is no (58, 87, large)-net in base 25, because
- 27 times m-reduction [i] would yield (58, 60, large)-net in base 25, but