Best Known (94−13, 94, s)-Nets in Base 7
(94−13, 94, 960806)-Net over F7 — Constructive and digital
Digital (81, 94, 960806)-net over F7, using
- 71 times duplication [i] based on digital (80, 93, 960806)-net over F7, using
- net defined by OOA [i] based on linear OOA(793, 960806, F7, 13, 13) (dual of [(960806, 13), 12490385, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(793, 5764837, F7, 13) (dual of [5764837, 5764744, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(8) [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(757, 5764801, F7, 9) (dual of [5764801, 5764744, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(74, 36, F7, 3) (dual of [36, 32, 4]-code or 36-cap in PG(3,7)), 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(793, 5764837, F7, 13) (dual of [5764837, 5764744, 14]-code), using
- net defined by OOA [i] based on linear OOA(793, 960806, F7, 13, 13) (dual of [(960806, 13), 12490385, 14]-NRT-code), using
(94−13, 94, 5764838)-Net over F7 — Digital
Digital (81, 94, 5764838)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(794, 5764838, F7, 13) (dual of [5764838, 5764744, 14]-code), using
- 1 times code embedding in larger space [i] based on linear OA(793, 5764837, F7, 13) (dual of [5764837, 5764744, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(8) [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(757, 5764801, F7, 9) (dual of [5764801, 5764744, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(74, 36, F7, 3) (dual of [36, 32, 4]-code or 36-cap in PG(3,7)), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(793, 5764837, F7, 13) (dual of [5764837, 5764744, 14]-code), using
(94−13, 94, large)-Net in Base 7 — Upper bound on s
There is no (81, 94, large)-net in base 7, because
- 11 times m-reduction [i] would yield (81, 83, large)-net in base 7, but