Best Known (74, 86, s)-Nets in Base 7
(74, 86, 960806)-Net over F7 — Constructive and digital
Digital (74, 86, 960806)-net over F7, using
- 71 times duplication [i] based on digital (73, 85, 960806)-net over F7, using
- net defined by OOA [i] based on linear OOA(785, 960806, F7, 12, 12) (dual of [(960806, 12), 11529587, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(785, 5764836, F7, 12) (dual of [5764836, 5764751, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(785, 5764837, F7, 12) (dual of [5764837, 5764752, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- linear OA(781, 5764801, F7, 12) (dual of [5764801, 5764720, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(749, 5764801, F7, 8) (dual of [5764801, 5764752, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(11) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(785, 5764837, F7, 12) (dual of [5764837, 5764752, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(785, 5764836, F7, 12) (dual of [5764836, 5764751, 13]-code), using
- net defined by OOA [i] based on linear OOA(785, 960806, F7, 12, 12) (dual of [(960806, 12), 11529587, 13]-NRT-code), using
(74, 86, 5764838)-Net over F7 — Digital
Digital (74, 86, 5764838)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(786, 5764838, F7, 12) (dual of [5764838, 5764752, 13]-code), using
- 1 times code embedding in larger space [i] based on linear OA(785, 5764837, F7, 12) (dual of [5764837, 5764752, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- linear OA(781, 5764801, F7, 12) (dual of [5764801, 5764720, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(749, 5764801, F7, 8) (dual of [5764801, 5764752, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(11) ⊂ Ce(7) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(785, 5764837, F7, 12) (dual of [5764837, 5764752, 13]-code), using
(74, 86, large)-Net in Base 7 — Upper bound on s
There is no (74, 86, large)-net in base 7, because
- 10 times m-reduction [i] would yield (74, 76, large)-net in base 7, but