Information on Result #1206321
Digital (228, 247, 932198)-net over F2, using (u, u+v)-construction based on
- digital (30, 39, 132)-net over F2, using
- net defined by OOA [i] based on linear OOA(239, 132, F2, 9, 9) (dual of [(132, 9), 1149, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(239, 132, F2, 8, 9) (dual of [(132, 8), 1017, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(239, 529, F2, 9) (dual of [529, 490, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(239, 531, F2, 9) (dual of [531, 492, 10]-code), using
- construction XX applied to C1 = C([509,4]), C2 = C([0,6]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([509,6]) [i] based on
- linear OA(228, 511, F2, 7) (dual of [511, 483, 8]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,4}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(228, 511, F2, 7) (dual of [511, 483, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(237, 511, F2, 9) (dual of [511, 474, 10]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,6}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(219, 511, F2, 5) (dual of [511, 492, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code) (see above)
- construction XX applied to C1 = C([509,4]), C2 = C([0,6]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([509,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(239, 531, F2, 9) (dual of [531, 492, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(239, 529, F2, 9) (dual of [529, 490, 10]-code), using
- appending kth column [i] based on linear OOA(239, 132, F2, 8, 9) (dual of [(132, 8), 1017, 10]-NRT-code), using
- net defined by OOA [i] based on linear OOA(239, 132, F2, 9, 9) (dual of [(132, 9), 1149, 10]-NRT-code), using
- digital (189, 208, 932066)-net over F2, using
- net defined by OOA [i] based on linear OOA(2208, 932066, F2, 19, 19) (dual of [(932066, 19), 17709046, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(2208, 8388595, F2, 19) (dual of [8388595, 8388387, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(2208, 8388595, F2, 19) (dual of [8388595, 8388387, 20]-code), using
- net defined by OOA [i] based on linear OOA(2208, 932066, F2, 19, 19) (dual of [(932066, 19), 17709046, 20]-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.