Best Known (13, 27, s)-Nets in Base 128
(13, 27, 2340)-Net over F128 — Constructive and digital
Digital (13, 27, 2340)-net over F128, using
- net defined by OOA [i] based on linear OOA(12827, 2340, F128, 14, 14) (dual of [(2340, 14), 32733, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(12827, 16380, F128, 14) (dual of [16380, 16353, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(12827, 16384, F128, 14) (dual of [16384, 16357, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(12827, 16384, F128, 14) (dual of [16384, 16357, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(12827, 16380, F128, 14) (dual of [16380, 16353, 15]-code), using
(13, 27, 4096)-Net over F128 — Digital
Digital (13, 27, 4096)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12827, 4096, F128, 4, 14) (dual of [(4096, 4), 16357, 15]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12827, 16384, F128, 14) (dual of [16384, 16357, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- OOA 4-folding [i] based on linear OA(12827, 16384, F128, 14) (dual of [16384, 16357, 15]-code), using
(13, 27, 3572106)-Net in Base 128 — Upper bound on s
There is no (13, 27, 3572107)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 784 637980 063293 493253 205366 653110 696500 175353 929265 384200 > 12827 [i]