Information on Result #3265937
Digital (58, 67, large)-net over F32, using 324 times duplication based on digital (54, 63, large)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 0, 262144)-net over F32, using
- s-reduction based on digital (0, 0, s)-net over F32 for arbitrarily large s, using
- digital (0, 0, 262144)-net over F32 (see above)
- digital (0, 0, 262144)-net over F32 (see above)
- digital (0, 0, 262144)-net over F32 (see above)
- digital (0, 0, 262144)-net over F32 (see above)
- digital (0, 0, 262144)-net over F32 (see above)
- digital (0, 0, 262144)-net over F32 (see above)
- digital (0, 0, 262144)-net over F32 (see above)
- digital (0, 0, 262144)-net over F32 (see above)
- digital (0, 0, 262144)-net over F32 (see above)
- digital (0, 0, 262144)-net over F32 (see above)
- digital (0, 0, 262144)-net over F32 (see above)
- digital (0, 0, 262144)-net over F32 (see above)
- digital (0, 0, 262144)-net over F32 (see above)
- digital (0, 0, 262144)-net over F32 (see above)
- digital (0, 0, 262144)-net over F32 (see above)
- digital (0, 0, 262144)-net over F32 (see above)
- digital (0, 0, 262144)-net over F32 (see above)
- digital (0, 0, 262144)-net over F32 (see above)
- digital (0, 0, 262144)-net over F32 (see above)
- digital (0, 0, 262144)-net over F32 (see above)
- digital (0, 0, 262144)-net over F32 (see above)
- digital (0, 0, 262144)-net over F32 (see above)
- digital (0, 1, 262144)-net over F32, using
- s-reduction based on digital (0, 1, s)-net over F32 for arbitrarily large s, using
- digital (0, 1, 262144)-net over F32 (see above)
- digital (0, 1, 262144)-net over F32 (see above)
- digital (0, 1, 262144)-net over F32 (see above)
- digital (0, 1, 262144)-net over F32 (see above)
- digital (3, 5, 262144)-net over F32, using
- s-reduction based on digital (3, 5, 1082401)-net over F32, using
- digital (4, 7, 262144)-net over F32, using
- s-reduction based on digital (4, 7, 1050624)-net over F32, using
- net defined by OOA [i] based on linear OOA(327, 1050624, F32, 3, 3) (dual of [(1050624, 3), 3151865, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(327, 1050624, F32, 2, 3) (dual of [(1050624, 2), 2101241, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(327, 1050624, F32, 3, 3) (dual of [(1050624, 3), 3151865, 4]-NRT-code), using
- s-reduction based on digital (4, 7, 1050624)-net over F32, using
- digital (9, 13, 262144)-net over F32, using
- s-reduction based on digital (9, 13, 524290)-net over F32, using
- net defined by OOA [i] based on linear OOA(3213, 524290, F32, 4, 4) (dual of [(524290, 4), 2097147, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(3213, 1048580, F32, 4) (dual of [1048580, 1048567, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(3213, 1048576, F32, 4) (dual of [1048576, 1048563, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(329, 1048576, F32, 3) (dual of [1048576, 1048567, 4]-code or 1048576-cap in PG(8,32)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(320, 4, F32, 0) (dual of [4, 4, 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
- OA 2-folding and stacking [i] based on linear OA(3213, 1048580, F32, 4) (dual of [1048580, 1048567, 5]-code), using
- net defined by OOA [i] based on linear OOA(3213, 524290, F32, 4, 4) (dual of [(524290, 4), 2097147, 5]-NRT-code), using
- s-reduction based on digital (9, 13, 524290)-net over F32, using
- digital (24, 33, 262144)-net over F32, using
- net defined by OOA [i] based on linear OOA(3233, 262144, F32, 9, 9) (dual of [(262144, 9), 2359263, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(3233, 1048577, F32, 9) (dual of [1048577, 1048544, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- OOA 4-folding and stacking with additional row [i] based on linear OA(3233, 1048577, F32, 9) (dual of [1048577, 1048544, 10]-code), using
- net defined by OOA [i] based on linear OOA(3233, 262144, F32, 9, 9) (dual of [(262144, 9), 2359263, 10]-NRT-code), using
- digital (0, 0, 262144)-net over F32, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, m and t.
Other Results with Identical Parameters
None.
Depending Results
None.