Best Known (83, 96, s)-Nets in Base 5
(83, 96, 325526)-Net over F5 — Constructive and digital
Digital (83, 96, 325526)-net over F5, using
- net defined by OOA [i] based on linear OOA(596, 325526, F5, 13, 13) (dual of [(325526, 13), 4231742, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(596, 1953157, F5, 13) (dual of [1953157, 1953061, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- linear OA(591, 1953125, F5, 13) (dual of [1953125, 1953034, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(564, 1953125, F5, 9) (dual of [1953125, 1953061, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(55, 32, F5, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- OOA 6-folding and stacking with additional row [i] based on linear OA(596, 1953157, F5, 13) (dual of [1953157, 1953061, 14]-code), using
(83, 96, 1335091)-Net over F5 — Digital
Digital (83, 96, 1335091)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(596, 1335091, F5, 13) (dual of [1335091, 1334995, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(596, 1953157, F5, 13) (dual of [1953157, 1953061, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- linear OA(591, 1953125, F5, 13) (dual of [1953125, 1953034, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(564, 1953125, F5, 9) (dual of [1953125, 1953061, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(55, 32, F5, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(596, 1953157, F5, 13) (dual of [1953157, 1953061, 14]-code), using
(83, 96, large)-Net in Base 5 — Upper bound on s
There is no (83, 96, large)-net in base 5, because
- 11 times m-reduction [i] would yield (83, 85, large)-net in base 5, but