Best Known (23, 47, s)-Nets in Base 128
(23, 47, 1365)-Net over F128 — Constructive and digital
Digital (23, 47, 1365)-net over F128, using
- net defined by OOA [i] based on linear OOA(12847, 1365, F128, 24, 24) (dual of [(1365, 24), 32713, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(12847, 16380, F128, 24) (dual of [16380, 16333, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(12847, 16384, F128, 24) (dual of [16384, 16337, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(12847, 16384, F128, 24) (dual of [16384, 16337, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(12847, 16380, F128, 24) (dual of [16380, 16333, 25]-code), using
(23, 47, 3659)-Net over F128 — Digital
Digital (23, 47, 3659)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12847, 3659, F128, 4, 24) (dual of [(3659, 4), 14589, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12847, 4096, F128, 4, 24) (dual of [(4096, 4), 16337, 25]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12847, 16384, F128, 24) (dual of [16384, 16337, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- OOA 4-folding [i] based on linear OA(12847, 16384, F128, 24) (dual of [16384, 16337, 25]-code), using
- discarding factors / shortening the dual code based on linear OOA(12847, 4096, F128, 4, 24) (dual of [(4096, 4), 16337, 25]-NRT-code), using
(23, 47, 7460989)-Net in Base 128 — Upper bound on s
There is no (23, 47, 7460990)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 1093 626663 145011 736027 763406 627562 011067 761978 373182 235596 205170 708800 217899 729270 634286 559768 462827 > 12847 [i]