Best Known (28−14, 28, s)-Nets in Base 128
(28−14, 28, 2341)-Net over F128 — Constructive and digital
Digital (14, 28, 2341)-net over F128, using
- net defined by OOA [i] based on linear OOA(12828, 2341, F128, 14, 14) (dual of [(2341, 14), 32746, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(12828, 16387, F128, 14) (dual of [16387, 16359, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(12828, 16389, F128, 14) (dual of [16389, 16361, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [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]
- linear OA(12823, 16384, F128, 12) (dual of [16384, 16361, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(12828, 16389, F128, 14) (dual of [16389, 16361, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(12828, 16387, F128, 14) (dual of [16387, 16359, 15]-code), using
(28−14, 28, 5463)-Net over F128 — Digital
Digital (14, 28, 5463)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12828, 5463, F128, 3, 14) (dual of [(5463, 3), 16361, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12828, 16389, F128, 14) (dual of [16389, 16361, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [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]
- linear OA(12823, 16384, F128, 12) (dual of [16384, 16361, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- OOA 3-folding [i] based on linear OA(12828, 16389, F128, 14) (dual of [16389, 16361, 15]-code), using
(28−14, 28, 7144216)-Net in Base 128 — Upper bound on s
There is no (14, 28, 7144217)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 100433 656024 226850 256472 724477 795304 084007 372114 841530 880264 > 12828 [i]