Best Known (76−26, 76, s)-Nets in Base 25
(76−26, 76, 1202)-Net over F25 — Constructive and digital
Digital (50, 76, 1202)-net over F25, using
- t-expansion [i] based on digital (49, 76, 1202)-net over F25, using
- net defined by OOA [i] based on linear OOA(2576, 1202, F25, 27, 27) (dual of [(1202, 27), 32378, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2576, 15627, F25, 27) (dual of [15627, 15551, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2576, 15628, F25, 27) (dual of [15628, 15552, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(2576, 15625, F25, 27) (dual of [15625, 15549, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(250, 3, F25, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(2576, 15628, F25, 27) (dual of [15628, 15552, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2576, 15627, F25, 27) (dual of [15627, 15551, 28]-code), using
- net defined by OOA [i] based on linear OOA(2576, 1202, F25, 27, 27) (dual of [(1202, 27), 32378, 28]-NRT-code), using
(76−26, 76, 9532)-Net over F25 — Digital
Digital (50, 76, 9532)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2576, 9532, F25, 26) (dual of [9532, 9456, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2576, 15637, F25, 26) (dual of [15637, 15561, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- 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(2564, 15625, F25, 22) (dual of [15625, 15561, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(253, 12, F25, 3) (dual of [12, 9, 4]-code or 12-arc in PG(2,25) or 12-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(2576, 15637, F25, 26) (dual of [15637, 15561, 27]-code), using
(76−26, 76, large)-Net in Base 25 — Upper bound on s
There is no (50, 76, large)-net in base 25, because
- 24 times m-reduction [i] would yield (50, 52, large)-net in base 25, but