Best Known (115, 115+22, s)-Nets in Base 8
(115, 115+22, 190652)-Net over F8 — Constructive and digital
Digital (115, 137, 190652)-net over F8, using
- net defined by OOA [i] based on linear OOA(8137, 190652, F8, 22, 22) (dual of [(190652, 22), 4194207, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(8137, 2097172, F8, 22) (dual of [2097172, 2097035, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(8137, 2097176, F8, 22) (dual of [2097176, 2097039, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(8134, 2097152, F8, 22) (dual of [2097152, 2097018, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(8113, 2097152, F8, 19) (dual of [2097152, 2097039, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(83, 24, F8, 2) (dual of [24, 21, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(8137, 2097176, F8, 22) (dual of [2097176, 2097039, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(8137, 2097172, F8, 22) (dual of [2097172, 2097035, 23]-code), using
(115, 115+22, 1641410)-Net over F8 — Digital
Digital (115, 137, 1641410)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8137, 1641410, F8, 22) (dual of [1641410, 1641273, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(8137, 2097176, F8, 22) (dual of [2097176, 2097039, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(8134, 2097152, F8, 22) (dual of [2097152, 2097018, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(8113, 2097152, F8, 19) (dual of [2097152, 2097039, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(83, 24, F8, 2) (dual of [24, 21, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(8137, 2097176, F8, 22) (dual of [2097176, 2097039, 23]-code), using
(115, 115+22, large)-Net in Base 8 — Upper bound on s
There is no (115, 137, large)-net in base 8, because
- 20 times m-reduction [i] would yield (115, 117, large)-net in base 8, but