Best Known (43−22, 43, s)-Nets in Base 128
(43−22, 43, 1489)-Net over F128 — Constructive and digital
Digital (21, 43, 1489)-net over F128, using
- net defined by OOA [i] based on linear OOA(12843, 1489, F128, 22, 22) (dual of [(1489, 22), 32715, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(12843, 16379, F128, 22) (dual of [16379, 16336, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(12843, 16384, F128, 22) (dual of [16384, 16341, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(12843, 16384, F128, 22) (dual of [16384, 16341, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(12843, 16379, F128, 22) (dual of [16379, 16336, 23]-code), using
(43−22, 43, 3850)-Net over F128 — Digital
Digital (21, 43, 3850)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12843, 3850, F128, 4, 22) (dual of [(3850, 4), 15357, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12843, 4096, F128, 4, 22) (dual of [(4096, 4), 16341, 23]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12843, 16384, F128, 22) (dual of [16384, 16341, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- OOA 4-folding [i] based on linear OA(12843, 16384, F128, 22) (dual of [16384, 16341, 23]-code), using
- discarding factors / shortening the dual code based on linear OOA(12843, 4096, F128, 4, 22) (dual of [(4096, 4), 16341, 23]-NRT-code), using
(43−22, 43, 6675525)-Net in Base 128 — Upper bound on s
There is no (21, 43, 6675526)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 4 074077 271299 339343 872430 729001 798584 240626 736665 611174 906186 852834 004090 514131 977766 974672 > 12843 [i]