Best Known (88, 110, s)-Nets in Base 7
(88, 110, 10696)-Net over F7 — Constructive and digital
Digital (88, 110, 10696)-net over F7, using
- net defined by OOA [i] based on linear OOA(7110, 10696, F7, 22, 22) (dual of [(10696, 22), 235202, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(7110, 117656, F7, 22) (dual of [117656, 117546, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(7109, 117649, F7, 22) (dual of [117649, 117540, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 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(71, 7, F7, 1) (dual of [7, 6, 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(21) ⊂ Ce(19) [i] based on
- OA 11-folding and stacking [i] based on linear OA(7110, 117656, F7, 22) (dual of [117656, 117546, 23]-code), using
(88, 110, 58828)-Net over F7 — Digital
Digital (88, 110, 58828)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(7110, 58828, F7, 2, 22) (dual of [(58828, 2), 117546, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(7110, 117656, F7, 22) (dual of [117656, 117546, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(7109, 117649, F7, 22) (dual of [117649, 117540, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 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(71, 7, F7, 1) (dual of [7, 6, 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(21) ⊂ Ce(19) [i] based on
- OOA 2-folding [i] based on linear OA(7110, 117656, F7, 22) (dual of [117656, 117546, 23]-code), using
(88, 110, large)-Net in Base 7 — Upper bound on s
There is no (88, 110, large)-net in base 7, because
- 20 times m-reduction [i] would yield (88, 90, large)-net in base 7, but