Best Known (52−17, 52, s)-Nets in Base 25
(52−17, 52, 1955)-Net over F25 — Constructive and digital
Digital (35, 52, 1955)-net over F25, using
- net defined by OOA [i] based on linear OOA(2552, 1955, F25, 17, 17) (dual of [(1955, 17), 33183, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2552, 15641, F25, 17) (dual of [15641, 15589, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(2549, 15626, F25, 17) (dual of [15626, 15577, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(2537, 15626, F25, 13) (dual of [15626, 15589, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(253, 15, F25, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,25) or 15-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 C([0,8]) ⊂ C([0,6]) [i] based on
- OOA 8-folding and stacking with additional row [i] based on linear OA(2552, 15641, F25, 17) (dual of [15641, 15589, 18]-code), using
(52−17, 52, 15148)-Net over F25 — Digital
Digital (35, 52, 15148)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2552, 15148, F25, 17) (dual of [15148, 15096, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2552, 15641, F25, 17) (dual of [15641, 15589, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(2549, 15626, F25, 17) (dual of [15626, 15577, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(2537, 15626, F25, 13) (dual of [15626, 15589, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(253, 15, F25, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,25) or 15-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 C([0,8]) ⊂ C([0,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2552, 15641, F25, 17) (dual of [15641, 15589, 18]-code), using
(52−17, 52, large)-Net in Base 25 — Upper bound on s
There is no (35, 52, large)-net in base 25, because
- 15 times m-reduction [i] would yield (35, 37, large)-net in base 25, but