Best Known (5, 5+6, s)-Nets in Base 128
(5, 5+6, 5462)-Net over F128 — Constructive and digital
Digital (5, 11, 5462)-net over F128, using
- net defined by OOA [i] based on linear OOA(12811, 5462, F128, 6, 6) (dual of [(5462, 6), 32761, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(12811, 16386, F128, 6) (dual of [16386, 16375, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(12811, 16384, F128, 6) (dual of [16384, 16373, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(1289, 16384, F128, 5) (dual of [16384, 16375, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- OA 3-folding and stacking [i] based on linear OA(12811, 16386, F128, 6) (dual of [16386, 16375, 7]-code), using
(5, 5+6, 8193)-Net over F128 — Digital
Digital (5, 11, 8193)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12811, 8193, F128, 2, 6) (dual of [(8193, 2), 16375, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12811, 16386, F128, 6) (dual of [16386, 16375, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(12811, 16384, F128, 6) (dual of [16384, 16373, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(1289, 16384, F128, 5) (dual of [16384, 16375, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- OOA 2-folding [i] based on linear OA(12811, 16386, F128, 6) (dual of [16386, 16375, 7]-code), using
(5, 5+6, 762107)-Net in Base 128 — Upper bound on s
There is no (5, 11, 762108)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 151116 269533 909591 709091 > 12811 [i]