Best Known (24, 24+12, s)-Nets in Base 25
(24, 24+12, 2606)-Net over F25 — Constructive and digital
Digital (24, 36, 2606)-net over F25, using
- net defined by OOA [i] based on linear OOA(2536, 2606, F25, 12, 12) (dual of [(2606, 12), 31236, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2536, 15636, F25, 12) (dual of [15636, 15600, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(2534, 15625, F25, 12) (dual of [15625, 15591, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2525, 15625, F25, 9) (dual of [15625, 15600, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(11) ⊂ Ce(8) [i] based on
- OA 6-folding and stacking [i] based on linear OA(2536, 15636, F25, 12) (dual of [15636, 15600, 13]-code), using
(24, 24+12, 14738)-Net over F25 — Digital
Digital (24, 36, 14738)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2536, 14738, F25, 12) (dual of [14738, 14702, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2536, 15636, F25, 12) (dual of [15636, 15600, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(2534, 15625, F25, 12) (dual of [15625, 15591, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2525, 15625, F25, 9) (dual of [15625, 15600, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(11) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(2536, 15636, F25, 12) (dual of [15636, 15600, 13]-code), using
(24, 24+12, large)-Net in Base 25 — Upper bound on s
There is no (24, 36, large)-net in base 25, because
- 10 times m-reduction [i] would yield (24, 26, large)-net in base 25, but