Best Known (79, 79+17, s)-Nets in Base 5
(79, 79+17, 9768)-Net over F5 — Constructive and digital
Digital (79, 96, 9768)-net over F5, using
- net defined by OOA [i] based on linear OOA(596, 9768, F5, 17, 17) (dual of [(9768, 17), 165960, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(596, 78145, F5, 17) (dual of [78145, 78049, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(596, 78150, F5, 17) (dual of [78150, 78054, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(592, 78125, F5, 17) (dual of [78125, 78033, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(571, 78125, F5, 13) (dual of [78125, 78054, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(54, 25, F5, 3) (dual of [25, 21, 4]-code or 25-cap in PG(3,5)), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(596, 78150, F5, 17) (dual of [78150, 78054, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(596, 78145, F5, 17) (dual of [78145, 78049, 18]-code), using
(79, 79+17, 42896)-Net over F5 — Digital
Digital (79, 96, 42896)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(596, 42896, F5, 17) (dual of [42896, 42800, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(596, 78150, F5, 17) (dual of [78150, 78054, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(592, 78125, F5, 17) (dual of [78125, 78033, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(571, 78125, F5, 13) (dual of [78125, 78054, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(54, 25, F5, 3) (dual of [25, 21, 4]-code or 25-cap in PG(3,5)), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(596, 78150, F5, 17) (dual of [78150, 78054, 18]-code), using
(79, 79+17, large)-Net in Base 5 — Upper bound on s
There is no (79, 96, large)-net in base 5, because
- 15 times m-reduction [i] would yield (79, 81, large)-net in base 5, but