Best Known (26, 26+12, s)-Nets in Base 25
(26, 26+12, 2607)-Net over F25 — Constructive and digital
Digital (26, 38, 2607)-net over F25, using
- net defined by OOA [i] based on linear OOA(2538, 2607, F25, 12, 12) (dual of [(2607, 12), 31246, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2538, 15642, F25, 12) (dual of [15642, 15604, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2538, 15644, F25, 12) (dual of [15644, 15606, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(6) [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(2519, 15625, F25, 7) (dual of [15625, 15606, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(254, 19, F25, 4) (dual of [19, 15, 5]-code or 19-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(11) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(2538, 15644, F25, 12) (dual of [15644, 15606, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(2538, 15642, F25, 12) (dual of [15642, 15604, 13]-code), using
(26, 26+12, 15644)-Net over F25 — Digital
Digital (26, 38, 15644)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2538, 15644, F25, 12) (dual of [15644, 15606, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(6) [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(2519, 15625, F25, 7) (dual of [15625, 15606, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(254, 19, F25, 4) (dual of [19, 15, 5]-code or 19-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(11) ⊂ Ce(6) [i] based on
(26, 26+12, large)-Net in Base 25 — Upper bound on s
There is no (26, 38, large)-net in base 25, because
- 10 times m-reduction [i] would yield (26, 28, large)-net in base 25, but