Best Known (34−12, 34, s)-Nets in Base 128
(34−12, 34, 349525)-Net over F128 — Constructive and digital
Digital (22, 34, 349525)-net over F128, using
- net defined by OOA [i] based on linear OOA(12834, 349525, F128, 12, 12) (dual of [(349525, 12), 4194266, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(12834, 2097150, F128, 12) (dual of [2097150, 2097116, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(12834, 2097152, F128, 12) (dual of [2097152, 2097118, 13]-code), using
- an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(12834, 2097152, F128, 12) (dual of [2097152, 2097118, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(12834, 2097150, F128, 12) (dual of [2097150, 2097116, 13]-code), using
(34−12, 34, 1014491)-Net over F128 — Digital
Digital (22, 34, 1014491)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12834, 1014491, F128, 2, 12) (dual of [(1014491, 2), 2028948, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12834, 1048577, F128, 2, 12) (dual of [(1048577, 2), 2097120, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12834, 2097154, F128, 12) (dual of [2097154, 2097120, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(12834, 2097155, F128, 12) (dual of [2097155, 2097121, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(12834, 2097152, F128, 12) (dual of [2097152, 2097118, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(12831, 2097152, F128, 11) (dual of [2097152, 2097121, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(11) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(12834, 2097155, F128, 12) (dual of [2097155, 2097121, 13]-code), using
- OOA 2-folding [i] based on linear OA(12834, 2097154, F128, 12) (dual of [2097154, 2097120, 13]-code), using
- discarding factors / shortening the dual code based on linear OOA(12834, 1048577, F128, 2, 12) (dual of [(1048577, 2), 2097120, 13]-NRT-code), using
(34−12, 34, large)-Net in Base 128 — Upper bound on s
There is no (22, 34, large)-net in base 128, because
- 10 times m-reduction [i] would yield (22, 24, large)-net in base 128, but