Best Known (51, 75, s)-Nets in Base 25
(51, 75, 1304)-Net over F25 — Constructive and digital
Digital (51, 75, 1304)-net over F25, using
- net defined by OOA [i] based on linear OOA(2575, 1304, F25, 24, 24) (dual of [(1304, 24), 31221, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2575, 15648, F25, 24) (dual of [15648, 15573, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- 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(2552, 15625, F25, 18) (dual of [15625, 15573, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(255, 23, F25, 5) (dual of [23, 18, 6]-code or 23-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(23) ⊂ Ce(17) [i] based on
- OA 12-folding and stacking [i] based on linear OA(2575, 15648, F25, 24) (dual of [15648, 15573, 25]-code), using
(51, 75, 15648)-Net over F25 — Digital
Digital (51, 75, 15648)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2575, 15648, F25, 24) (dual of [15648, 15573, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- 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(2552, 15625, F25, 18) (dual of [15625, 15573, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(255, 23, F25, 5) (dual of [23, 18, 6]-code or 23-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(23) ⊂ Ce(17) [i] based on
(51, 75, large)-Net in Base 25 — Upper bound on s
There is no (51, 75, large)-net in base 25, because
- 22 times m-reduction [i] would yield (51, 53, large)-net in base 25, but