Best Known (79, 79+13, s)-Nets in Base 7
(79, 79+13, 960804)-Net over F7 — Constructive and digital
Digital (79, 92, 960804)-net over F7, using
- net defined by OOA [i] based on linear OOA(792, 960804, F7, 13, 13) (dual of [(960804, 13), 12490360, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(792, 5764825, F7, 13) (dual of [5764825, 5764733, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(792, 5764828, F7, 13) (dual of [5764828, 5764736, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(789, 5764801, F7, 13) (dual of [5764801, 5764712, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(765, 5764801, F7, 10) (dual of [5764801, 5764736, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(73, 27, F7, 2) (dual of [27, 24, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(792, 5764828, F7, 13) (dual of [5764828, 5764736, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(792, 5764825, F7, 13) (dual of [5764825, 5764733, 14]-code), using
(79, 79+13, 5764828)-Net over F7 — Digital
Digital (79, 92, 5764828)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(792, 5764828, F7, 13) (dual of [5764828, 5764736, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(789, 5764801, F7, 13) (dual of [5764801, 5764712, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(765, 5764801, F7, 10) (dual of [5764801, 5764736, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(73, 27, F7, 2) (dual of [27, 24, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
(79, 79+13, large)-Net in Base 7 — Upper bound on s
There is no (79, 92, large)-net in base 7, because
- 11 times m-reduction [i] would yield (79, 81, large)-net in base 7, but