Best Known (85, 85+11, s)-Nets in Base 5
(85, 85+11, 1678321)-Net over F5 — Constructive and digital
Digital (85, 96, 1678321)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (10, 15, 601)-net over F5, using
- net defined by OOA [i] based on linear OOA(515, 601, F5, 5, 5) (dual of [(601, 5), 2990, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(515, 1203, F5, 5) (dual of [1203, 1188, 6]-code), using
- 1 times code embedding in larger space [i] based on linear OA(514, 1202, F5, 5) (dual of [1202, 1188, 6]-code), using
- trace code [i] based on linear OA(257, 601, F25, 5) (dual of [601, 594, 6]-code), using
- 1 times code embedding in larger space [i] based on linear OA(514, 1202, F5, 5) (dual of [1202, 1188, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(515, 1203, F5, 5) (dual of [1203, 1188, 6]-code), using
- net defined by OOA [i] based on linear OOA(515, 601, F5, 5, 5) (dual of [(601, 5), 2990, 6]-NRT-code), using
- digital (70, 81, 1677720)-net over F5, using
- net defined by OOA [i] based on linear OOA(581, 1677720, F5, 11, 11) (dual of [(1677720, 11), 18454839, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(581, 8388601, F5, 11) (dual of [8388601, 8388520, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(581, large, F5, 11) (dual of [large, large−81, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 520−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(581, large, F5, 11) (dual of [large, large−81, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(581, 8388601, F5, 11) (dual of [8388601, 8388520, 12]-code), using
- net defined by OOA [i] based on linear OOA(581, 1677720, F5, 11, 11) (dual of [(1677720, 11), 18454839, 12]-NRT-code), using
- digital (10, 15, 601)-net over F5, using
(85, 85+11, large)-Net over F5 — Digital
Digital (85, 96, large)-net over F5, using
- 56 times duplication [i] based on digital (79, 90, large)-net over F5, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(590, large, F5, 11) (dual of [large, large−90, 12]-code), using
- 9 times code embedding in larger space [i] based on linear OA(581, large, F5, 11) (dual of [large, large−81, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 520−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- 9 times code embedding in larger space [i] based on linear OA(581, large, F5, 11) (dual of [large, large−81, 12]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(590, large, F5, 11) (dual of [large, large−90, 12]-code), using
(85, 85+11, large)-Net in Base 5 — Upper bound on s
There is no (85, 96, large)-net in base 5, because
- 9 times m-reduction [i] would yield (85, 87, large)-net in base 5, but