Best Known (14, 14+6, s)-Nets in Base 128
(14, 14+6, 715436)-Net over F128 — Constructive and digital
Digital (14, 20, 715436)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 4, 16385)-net over F128, using
- net defined by OOA [i] based on linear OOA(1284, 16385, F128, 3, 3) (dual of [(16385, 3), 49151, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(1284, 16385, F128, 2, 3) (dual of [(16385, 2), 32766, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(1284, 16385, F128, 3, 3) (dual of [(16385, 3), 49151, 4]-NRT-code), using
- digital (10, 16, 699051)-net over F128, using
- net defined by OOA [i] based on linear OOA(12816, 699051, F128, 6, 6) (dual of [(699051, 6), 4194290, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(12816, 2097153, F128, 6) (dual of [2097153, 2097137, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(12816, 2097155, F128, 6) (dual of [2097155, 2097139, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(12816, 2097152, F128, 6) (dual of [2097152, 2097136, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(12813, 2097152, F128, 5) (dual of [2097152, 2097139, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 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
- discarding factors / shortening the dual code based on linear OA(12816, 2097155, F128, 6) (dual of [2097155, 2097139, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(12816, 2097153, F128, 6) (dual of [2097153, 2097137, 7]-code), using
- net defined by OOA [i] based on linear OOA(12816, 699051, F128, 6, 6) (dual of [(699051, 6), 4194290, 7]-NRT-code), using
- digital (1, 4, 16385)-net over F128, using
(14, 14+6, 2796201)-Net in Base 128 — Constructive
(14, 20, 2796201)-net in base 128, using
- 1281 times duplication [i] based on (13, 19, 2796201)-net in base 128, using
- net defined by OOA [i] based on OOA(12819, 2796201, S128, 6, 6), using
- OA 3-folding and stacking [i] based on OA(12819, large, S128, 6), using
- discarding parts of the base [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding parts of the base [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- OA 3-folding and stacking [i] based on OA(12819, large, S128, 6), using
- net defined by OOA [i] based on OOA(12819, 2796201, S128, 6, 6), using
(14, 14+6, 5506461)-Net over F128 — Digital
Digital (14, 20, 5506461)-net over F128, using
(14, 14+6, 8388602)-Net in Base 128
(14, 20, 8388602)-net in base 128, using
- 1281 times duplication [i] based on (13, 19, 8388602)-net in base 128, using
- net defined by OOA [i] based on OOA(12819, 8388602, S128, 9, 6), using
- OOA stacking with additional row [i] based on OOA(12819, large, S128, 3, 6), using
- discarding parts of the base [i] based on linear OOA(25616, large, F256, 3, 6), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- discarding parts of the base [i] based on linear OOA(25616, large, F256, 3, 6), using
- OOA stacking with additional row [i] based on OOA(12819, large, S128, 3, 6), using
- net defined by OOA [i] based on OOA(12819, 8388602, S128, 9, 6), using
(14, 14+6, large)-Net in Base 128 — Upper bound on s
There is no (14, 20, large)-net in base 128, because
- 4 times m-reduction [i] would yield (14, 16, large)-net in base 128, but