Best Known (55, 84, s)-Nets in Base 25
(55, 84, 1116)-Net over F25 — Constructive and digital
Digital (55, 84, 1116)-net over F25, using
- 252 times duplication [i] based on digital (53, 82, 1116)-net over F25, using
- net defined by OOA [i] based on linear OOA(2582, 1116, F25, 29, 29) (dual of [(1116, 29), 32282, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [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]
- OOA 14-folding and stacking with additional row [i] based on linear OA(2582, 15625, F25, 29) (dual of [15625, 15543, 30]-code), using
- net defined by OOA [i] based on linear OOA(2582, 1116, F25, 29, 29) (dual of [(1116, 29), 32282, 30]-NRT-code), using
(55, 84, 9014)-Net over F25 — Digital
Digital (55, 84, 9014)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2584, 9014, F25, 29) (dual of [9014, 8930, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2584, 15636, F25, 29) (dual of [15636, 15552, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(25) [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(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(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(28) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(2584, 15636, F25, 29) (dual of [15636, 15552, 30]-code), using
(55, 84, large)-Net in Base 25 — Upper bound on s
There is no (55, 84, large)-net in base 25, because
- 27 times m-reduction [i] would yield (55, 57, large)-net in base 25, but