Best Known (6, 6+6, s)-Nets in Base 128
(6, 6+6, 5463)-Net over F128 — Constructive and digital
Digital (6, 12, 5463)-net over F128, using
- net defined by OOA [i] based on linear OOA(12812, 5463, F128, 6, 6) (dual of [(5463, 6), 32766, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(12812, 16389, F128, 6) (dual of [16389, 16377, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(3) [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(1287, 16384, F128, 4) (dual of [16384, 16377, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(5) ⊂ Ce(3) [i] based on
- OA 3-folding and stacking [i] based on linear OA(12812, 16389, F128, 6) (dual of [16389, 16377, 7]-code), using
(6, 6+6, 10865)-Net over F128 — Digital
Digital (6, 12, 10865)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12812, 10865, F128, 6) (dual of [10865, 10853, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(12812, 16389, F128, 6) (dual of [16389, 16377, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(3) [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(1287, 16384, F128, 4) (dual of [16384, 16377, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(5) ⊂ Ce(3) [i] based on
- discarding factors / shortening the dual code based on linear OA(12812, 16389, F128, 6) (dual of [16389, 16377, 7]-code), using
(6, 6+6, 3840783)-Net in Base 128 — Upper bound on s
There is no (6, 12, 3840784)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 19 342825 373850 917118 817465 > 12812 [i]