Best Known (22−8, 22, s)-Nets in Base 128
(22−8, 22, 524288)-Net over F128 — Constructive and digital
Digital (14, 22, 524288)-net over F128, using
- net defined by OOA [i] based on linear OOA(12822, 524288, F128, 8, 8) (dual of [(524288, 8), 4194282, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(12822, 2097152, F128, 8) (dual of [2097152, 2097130, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OA 4-folding and stacking [i] based on linear OA(12822, 2097152, F128, 8) (dual of [2097152, 2097130, 9]-code), using
(22−8, 22, 1048577)-Net over F128 — Digital
Digital (14, 22, 1048577)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12822, 1048577, F128, 2, 8) (dual of [(1048577, 2), 2097132, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12822, 2097154, F128, 8) (dual of [2097154, 2097132, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(12822, 2097155, F128, 8) (dual of [2097155, 2097133, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(12822, 2097152, F128, 8) (dual of [2097152, 2097130, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(12819, 2097152, F128, 7) (dual of [2097152, 2097133, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(12822, 2097155, F128, 8) (dual of [2097155, 2097133, 9]-code), using
- OOA 2-folding [i] based on linear OA(12822, 2097154, F128, 8) (dual of [2097154, 2097132, 9]-code), using
(22−8, 22, large)-Net in Base 128 — Upper bound on s
There is no (14, 22, large)-net in base 128, because
- 6 times m-reduction [i] would yield (14, 16, large)-net in base 128, but