Information on Result #1233719
Digital (89, 102, 2815721)-net over F32, using generalized (u, u+v)-construction based on
- digital (2, 5, 3136)-net over F32, using
- net defined by OOA [i] based on linear OOA(325, 3136, F32, 3, 3) (dual of [(3136, 3), 9403, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(325, 3136, F32, 2, 3) (dual of [(3136, 2), 6267, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(325, 3136, F32, 3, 3) (dual of [(3136, 3), 9403, 4]-NRT-code), using
- digital (6, 10, 16385)-net over F32, using
- net defined by OOA [i] based on linear OOA(3210, 16385, F32, 4, 4) (dual of [(16385, 4), 65530, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(3210, 32770, F32, 4) (dual of [32770, 32760, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(3210, 32771, F32, 4) (dual of [32771, 32761, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(3210, 32768, F32, 4) (dual of [32768, 32758, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(327, 32768, F32, 3) (dual of [32768, 32761, 4]-code or 32768-cap in PG(6,32)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(320, 3, F32, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(3210, 32771, F32, 4) (dual of [32771, 32761, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(3210, 32770, F32, 4) (dual of [32770, 32760, 5]-code), using
- net defined by OOA [i] based on linear OOA(3210, 16385, F32, 4, 4) (dual of [(16385, 4), 65530, 5]-NRT-code), using
- digital (20, 26, 1398100)-net over F32, using
- s-reduction based on digital (20, 26, 2796201)-net over F32, using
- net defined by OOA [i] based on linear OOA(3226, 2796201, F32, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(3226, large, F32, 6) (dual of [large, large−26, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(3226, large, F32, 6) (dual of [large, large−26, 7]-code), using
- net defined by OOA [i] based on linear OOA(3226, 2796201, F32, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- s-reduction based on digital (20, 26, 2796201)-net over F32, using
- digital (48, 61, 1398100)-net over F32, using
- net defined by OOA [i] based on linear OOA(3261, 1398100, F32, 13, 13) (dual of [(1398100, 13), 18175239, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3261, 8388601, F32, 13) (dual of [8388601, 8388540, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3261, large, F32, 13) (dual of [large, large−61, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3261, large, F32, 13) (dual of [large, large−61, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3261, 8388601, F32, 13) (dual of [8388601, 8388540, 14]-code), using
- net defined by OOA [i] based on linear OOA(3261, 1398100, F32, 13, 13) (dual of [(1398100, 13), 18175239, 14]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.