Information on Result #1224642
Digital (60, 69, 4227164)-net over F32, using (u, u+v)-construction based on
- digital (12, 16, 4194301)-net over F32, using
- net defined by OOA [i] based on linear OOA(3216, 4194301, F32, 4, 4) (dual of [(4194301, 4), 16777188, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(3216, 8388602, F32, 4) (dual of [8388602, 8388586, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(3216, large, F32, 4) (dual of [large, large−16, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(3216, large, F32, 4) (dual of [large, large−16, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(3216, 8388602, F32, 4) (dual of [8388602, 8388586, 5]-code), using
- net defined by OOA [i] based on linear OOA(3216, 4194301, F32, 4, 4) (dual of [(4194301, 4), 16777188, 5]-NRT-code), using
- digital (44, 53, 2113582)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (8, 12, 16432)-net over F32, using
- net defined by OOA [i] based on linear OOA(3212, 16432, F32, 4, 4) (dual of [(16432, 4), 65716, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(3212, 32864, F32, 4) (dual of [32864, 32852, 5]-code), using
- generalized (u, u+v)-construction [i] based on
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 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
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(321, 1027, F32, 1) (dual of [1027, 1026, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(321, 1027, F32, 1) (dual of [1027, 1026, 2]-code) (see above)
- linear OA(323, 1027, F32, 2) (dual of [1027, 1024, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(323, 1057, F32, 2) (dual of [1057, 1054, 3]-code), using
- Hamming code H(3,32) [i]
- discarding factors / shortening the dual code based on linear OA(323, 1057, F32, 2) (dual of [1057, 1054, 3]-code), using
- linear OA(327, 1027, F32, 4) (dual of [1027, 1020, 5]-code), using
- construction XX applied to C1 = C([1022,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([1022,2]) [i] based on
- linear OA(325, 1023, F32, 3) (dual of [1023, 1018, 4]-code or 1023-cap in PG(4,32)), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,1}, and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(325, 1023, F32, 3) (dual of [1023, 1018, 4]-code or 1023-cap in PG(4,32)), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(327, 1023, F32, 4) (dual of [1023, 1016, 5]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(323, 1023, F32, 2) (dual of [1023, 1020, 3]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 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 (see above)
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([1022,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([1022,2]) [i] based on
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code), using
- generalized (u, u+v)-construction [i] based on
- OA 2-folding and stacking [i] based on linear OA(3212, 32864, F32, 4) (dual of [32864, 32852, 5]-code), using
- net defined by OOA [i] based on linear OOA(3212, 16432, F32, 4, 4) (dual of [(16432, 4), 65716, 5]-NRT-code), using
- digital (32, 41, 2097150)-net over F32, using
- net defined by OOA [i] based on linear OOA(3241, 2097150, F32, 9, 9) (dual of [(2097150, 9), 18874309, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(3241, 8388601, F32, 9) (dual of [8388601, 8388560, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(3241, large, F32, 9) (dual of [large, large−41, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3241, large, F32, 9) (dual of [large, large−41, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(3241, 8388601, F32, 9) (dual of [8388601, 8388560, 10]-code), using
- net defined by OOA [i] based on linear OOA(3241, 2097150, F32, 9, 9) (dual of [(2097150, 9), 18874309, 10]-NRT-code), using
- digital (8, 12, 16432)-net over F32, using
- (u, u+v)-construction [i] based on
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.