Best Known (80, 80+18, s)-Nets in Base 7
(80, 80+18, 13076)-Net over F7 — Constructive and digital
Digital (80, 98, 13076)-net over F7, using
- net defined by OOA [i] based on linear OOA(798, 13076, F7, 18, 18) (dual of [(13076, 18), 235270, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(798, 117684, F7, 18) (dual of [117684, 117586, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(798, 117686, F7, 18) (dual of [117686, 117588, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(11) [i] based on
- linear OA(791, 117649, F7, 18) (dual of [117649, 117558, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(761, 117649, F7, 12) (dual of [117649, 117588, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(77, 37, F7, 5) (dual of [37, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- construction X applied to Ce(17) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(798, 117686, F7, 18) (dual of [117686, 117588, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(798, 117684, F7, 18) (dual of [117684, 117586, 19]-code), using
(80, 80+18, 117686)-Net over F7 — Digital
Digital (80, 98, 117686)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(798, 117686, F7, 18) (dual of [117686, 117588, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(11) [i] based on
- linear OA(791, 117649, F7, 18) (dual of [117649, 117558, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(761, 117649, F7, 12) (dual of [117649, 117588, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(77, 37, F7, 5) (dual of [37, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- construction X applied to Ce(17) ⊂ Ce(11) [i] based on
(80, 80+18, large)-Net in Base 7 — Upper bound on s
There is no (80, 98, large)-net in base 7, because
- 16 times m-reduction [i] would yield (80, 82, large)-net in base 7, but