Best Known (86−13, 86, s)-Nets in Base 7
(86−13, 86, 137272)-Net over F7 — Constructive and digital
Digital (73, 86, 137272)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (1, 7, 13)-net over F7, using
- 6 times m-reduction [i] based on digital (1, 13, 13)-net over F7, using
- digital (66, 79, 137259)-net over F7, using
- net defined by OOA [i] based on linear OOA(779, 137259, F7, 13, 13) (dual of [(137259, 13), 1784288, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(779, 823555, F7, 13) (dual of [823555, 823476, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(779, 823558, F7, 13) (dual of [823558, 823479, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(778, 823543, F7, 13) (dual of [823543, 823465, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(764, 823543, F7, 11) (dual of [823543, 823479, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(71, 15, F7, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(779, 823558, F7, 13) (dual of [823558, 823479, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(779, 823555, F7, 13) (dual of [823555, 823476, 14]-code), using
- net defined by OOA [i] based on linear OOA(779, 137259, F7, 13, 13) (dual of [(137259, 13), 1784288, 14]-NRT-code), using
- digital (1, 7, 13)-net over F7, using
(86−13, 86, 1004035)-Net over F7 — Digital
Digital (73, 86, 1004035)-net over F7, using
(86−13, 86, large)-Net in Base 7 — Upper bound on s
There is no (73, 86, large)-net in base 7, because
- 11 times m-reduction [i] would yield (73, 75, large)-net in base 7, but