Best Known (35, 48, s)-Nets in Base 128
(35, 48, 354987)-Net over F128 — Constructive and digital
Digital (35, 48, 354987)-net over F128, using
- (u, u+v)-construction [i] based on
- 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
- net defined by OOA [i] based on linear OOA(12811, 5462, F128, 6, 6) (dual of [(5462, 6), 32761, 7]-NRT-code), using
- digital (24, 37, 349525)-net over F128, using
- net defined by OOA [i] based on linear OOA(12837, 349525, F128, 13, 13) (dual of [(349525, 13), 4543788, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(12837, 2097151, F128, 13) (dual of [2097151, 2097114, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(12837, 2097152, F128, 13) (dual of [2097152, 2097115, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(12837, 2097152, F128, 13) (dual of [2097152, 2097115, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(12837, 2097151, F128, 13) (dual of [2097151, 2097114, 14]-code), using
- net defined by OOA [i] based on linear OOA(12837, 349525, F128, 13, 13) (dual of [(349525, 13), 4543788, 14]-NRT-code), using
- digital (5, 11, 5462)-net over F128, using
(35, 48, 1398100)-Net in Base 128 — Constructive
(35, 48, 1398100)-net in base 128, using
- base change [i] based on digital (29, 42, 1398100)-net over F256, using
- 2565 times duplication [i] based on digital (24, 37, 1398100)-net over F256, using
- net defined by OOA [i] based on linear OOA(25637, 1398100, F256, 13, 13) (dual of [(1398100, 13), 18175263, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(25637, 8388601, F256, 13) (dual of [8388601, 8388564, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(25637, large, F256, 13) (dual of [large, large−37, 14]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(25637, large, F256, 13) (dual of [large, large−37, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(25637, 8388601, F256, 13) (dual of [8388601, 8388564, 14]-code), using
- net defined by OOA [i] based on linear OOA(25637, 1398100, F256, 13, 13) (dual of [(1398100, 13), 18175263, 14]-NRT-code), using
- 2565 times duplication [i] based on digital (24, 37, 1398100)-net over F256, using
(35, 48, large)-Net over F128 — Digital
Digital (35, 48, large)-net over F128, using
(35, 48, large)-Net in Base 128 — Upper bound on s
There is no (35, 48, large)-net in base 128, because
- 11 times m-reduction [i] would yield (35, 37, large)-net in base 128, but