Best Known (29, 29+30, s)-Nets in Base 128
(29, 29+30, 1092)-Net over F128 — Constructive and digital
Digital (29, 59, 1092)-net over F128, using
- net defined by OOA [i] based on linear OOA(12859, 1092, F128, 30, 30) (dual of [(1092, 30), 32701, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(12859, 16380, F128, 30) (dual of [16380, 16321, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(12859, 16384, F128, 30) (dual of [16384, 16325, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(12859, 16384, F128, 30) (dual of [16384, 16325, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(12859, 16380, F128, 30) (dual of [16380, 16321, 31]-code), using
(29, 29+30, 3453)-Net over F128 — Digital
Digital (29, 59, 3453)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12859, 3453, F128, 4, 30) (dual of [(3453, 4), 13753, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12859, 4096, F128, 4, 30) (dual of [(4096, 4), 16325, 31]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12859, 16384, F128, 30) (dual of [16384, 16325, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- OOA 4-folding [i] based on linear OA(12859, 16384, F128, 30) (dual of [16384, 16325, 31]-code), using
- discarding factors / shortening the dual code based on linear OOA(12859, 4096, F128, 4, 30) (dual of [(4096, 4), 16325, 31]-NRT-code), using
(29, 29+30, large)-Net in Base 128 — Upper bound on s
There is no (29, 59, large)-net in base 128, because
- 28 times m-reduction [i] would yield (29, 31, large)-net in base 128, but