Best Known (82, 82+13, s)-Nets in Base 5
(82, 82+13, 325525)-Net over F5 — Constructive and digital
Digital (82, 95, 325525)-net over F5, using
- net defined by OOA [i] based on linear OOA(595, 325525, F5, 13, 13) (dual of [(325525, 13), 4231730, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(595, 1953151, F5, 13) (dual of [1953151, 1953056, 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(54, 26, F5, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), 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(595, 1953151, F5, 13) (dual of [1953151, 1953056, 14]-code), using
(82, 82+13, 1153368)-Net over F5 — Digital
Digital (82, 95, 1153368)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(595, 1153368, F5, 13) (dual of [1153368, 1153273, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(595, 1953151, F5, 13) (dual of [1953151, 1953056, 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(54, 26, F5, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(595, 1953151, F5, 13) (dual of [1953151, 1953056, 14]-code), using
(82, 82+13, large)-Net in Base 5 — Upper bound on s
There is no (82, 95, large)-net in base 5, because
- 11 times m-reduction [i] would yield (82, 84, large)-net in base 5, but