Best Known (14, 14+15, s)-Nets in Base 128
(14, 14+15, 2340)-Net over F128 — Constructive and digital
Digital (14, 29, 2340)-net over F128, using
- net defined by OOA [i] based on linear OOA(12829, 2340, F128, 15, 15) (dual of [(2340, 15), 35071, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(12829, 16381, F128, 15) (dual of [16381, 16352, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(12829, 16384, F128, 15) (dual of [16384, 16355, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(12829, 16384, F128, 15) (dual of [16384, 16355, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(12829, 16381, F128, 15) (dual of [16381, 16352, 16]-code), using
(14, 14+15, 4096)-Net over F128 — Digital
Digital (14, 29, 4096)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12829, 4096, F128, 4, 15) (dual of [(4096, 4), 16355, 16]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12829, 16384, F128, 15) (dual of [16384, 16355, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- OOA 4-folding [i] based on linear OA(12829, 16384, F128, 15) (dual of [16384, 16355, 16]-code), using
(14, 14+15, 7144216)-Net in Base 128 — Upper bound on s
There is no (14, 29, 7144217)-net in base 128, because
- 1 times m-reduction [i] would yield (14, 28, 7144217)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 100433 656024 226850 256472 724477 795304 084007 372114 841530 880264 > 12828 [i]