Best Known (30, 42, s)-Nets in Base 128
(30, 42, 349676)-Net over F128 — Constructive and digital
Digital (30, 42, 349676)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 7, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- digital (23, 35, 349526)-net over F128, using
- net defined by OOA [i] based on linear OOA(12835, 349526, F128, 12, 12) (dual of [(349526, 12), 4194277, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(12835, 2097156, F128, 12) (dual of [2097156, 2097121, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(12835, 2097159, F128, 12) (dual of [2097159, 2097124, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(12834, 2097152, F128, 12) (dual of [2097152, 2097118, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(12828, 2097152, F128, 10) (dual of [2097152, 2097124, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 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(11) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(12835, 2097159, F128, 12) (dual of [2097159, 2097124, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(12835, 2097156, F128, 12) (dual of [2097156, 2097121, 13]-code), using
- net defined by OOA [i] based on linear OOA(12835, 349526, F128, 12, 12) (dual of [(349526, 12), 4194277, 13]-NRT-code), using
- digital (1, 7, 150)-net over F128, using
(30, 42, 1398100)-Net in Base 128 — Constructive
(30, 42, 1398100)-net in base 128, using
- 1 times m-reduction [i] based on (30, 43, 1398100)-net in base 128, using
- net defined by OOA [i] based on OOA(12843, 1398100, S128, 13, 13), using
- OOA 6-folding and stacking with additional row [i] based on OA(12843, 8388601, S128, 13), using
- discarding factors based on OA(12843, large, S128, 13), using
- discarding parts of the base [i] 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 parts of the base [i] based on linear OA(25637, large, F256, 13) (dual of [large, large−37, 14]-code), using
- discarding factors based on OA(12843, large, S128, 13), using
- OOA 6-folding and stacking with additional row [i] based on OA(12843, 8388601, S128, 13), using
- net defined by OOA [i] based on OOA(12843, 1398100, S128, 13, 13), using
(30, 42, 4294591)-Net over F128 — Digital
Digital (30, 42, 4294591)-net over F128, using
(30, 42, large)-Net in Base 128 — Upper bound on s
There is no (30, 42, large)-net in base 128, because
- 10 times m-reduction [i] would yield (30, 32, large)-net in base 128, but