Best Known (86, 106, s)-Nets in Base 7
(86, 106, 11767)-Net over F7 — Constructive and digital
Digital (86, 106, 11767)-net over F7, using
- net defined by OOA [i] based on linear OOA(7106, 11767, F7, 20, 20) (dual of [(11767, 20), 235234, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(7106, 117670, F7, 20) (dual of [117670, 117564, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- linear OA(7103, 117649, F7, 20) (dual of [117649, 117546, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(785, 117649, F7, 17) (dual of [117649, 117564, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(73, 21, F7, 2) (dual of [21, 18, 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(19) ⊂ Ce(16) [i] based on
- OA 10-folding and stacking [i] based on linear OA(7106, 117670, F7, 20) (dual of [117670, 117564, 21]-code), using
(86, 106, 107071)-Net over F7 — Digital
Digital (86, 106, 107071)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(7106, 107071, F7, 20) (dual of [107071, 106965, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(7106, 117670, F7, 20) (dual of [117670, 117564, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- linear OA(7103, 117649, F7, 20) (dual of [117649, 117546, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(785, 117649, F7, 17) (dual of [117649, 117564, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(73, 21, F7, 2) (dual of [21, 18, 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(19) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(7106, 117670, F7, 20) (dual of [117670, 117564, 21]-code), using
(86, 106, large)-Net in Base 7 — Upper bound on s
There is no (86, 106, large)-net in base 7, because
- 18 times m-reduction [i] would yield (86, 88, large)-net in base 7, but