Information on Result #1232982
Digital (97, 110, 5592480)-net over F32, using generalized (u, u+v)-construction based on
- digital (0, 0, 174765)-net over F32, using
- s-reduction based on digital (0, 0, s)-net over F32 for arbitrarily large s, using
- digital (0, 0, 174765)-net over F32 (see above)
- digital (0, 0, 174765)-net over F32 (see above)
- digital (0, 0, 174765)-net over F32 (see above)
- digital (0, 0, 174765)-net over F32 (see above)
- digital (0, 0, 174765)-net over F32 (see above)
- digital (0, 0, 174765)-net over F32 (see above)
- digital (0, 0, 174765)-net over F32 (see above)
- digital (0, 0, 174765)-net over F32 (see above)
- digital (0, 0, 174765)-net over F32 (see above)
- digital (0, 0, 174765)-net over F32 (see above)
- digital (0, 0, 174765)-net over F32 (see above)
- digital (0, 0, 174765)-net over F32 (see above)
- digital (0, 0, 174765)-net over F32 (see above)
- digital (0, 0, 174765)-net over F32 (see above)
- digital (0, 0, 174765)-net over F32 (see above)
- digital (0, 0, 174765)-net over F32 (see above)
- digital (0, 0, 174765)-net over F32 (see above)
- digital (0, 0, 174765)-net over F32 (see above)
- digital (0, 1, 174765)-net over F32, using
- s-reduction based on digital (0, 1, s)-net over F32 for arbitrarily large s, using
- digital (0, 1, 174765)-net over F32 (see above)
- digital (0, 1, 174765)-net over F32 (see above)
- digital (0, 1, 174765)-net over F32 (see above)
- digital (0, 1, 174765)-net over F32 (see above)
- digital (0, 1, 174765)-net over F32 (see above)
- digital (0, 1, 174765)-net over F32 (see above)
- digital (3, 5, 174765)-net over F32, using
- s-reduction based on digital (3, 5, 1082401)-net over F32, using
- digital (3, 5, 174765)-net over F32 (see above)
- digital (4, 7, 174765)-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, 174765)-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 (15, 21, 174765)-net over F32, using
- s-reduction based on digital (15, 21, 349526)-net over F32, using
- net defined by OOA [i] based on linear OOA(3221, 349526, F32, 6, 6) (dual of [(349526, 6), 2097135, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(3221, 1048578, F32, 6) (dual of [1048578, 1048557, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(3221, 1048580, F32, 6) (dual of [1048580, 1048559, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(3221, 1048576, F32, 6) (dual of [1048576, 1048555, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(3217, 1048576, F32, 5) (dual of [1048576, 1048559, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(320, 4, F32, 0) (dual of [4, 4, 1]-code) (see above)
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(3221, 1048580, F32, 6) (dual of [1048580, 1048559, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(3221, 1048578, F32, 6) (dual of [1048578, 1048557, 7]-code), using
- net defined by OOA [i] based on linear OOA(3221, 349526, F32, 6, 6) (dual of [(349526, 6), 2097135, 7]-NRT-code), using
- s-reduction based on digital (15, 21, 349526)-net over F32, using
- digital (39, 52, 174765)-net over F32, using
- net defined by OOA [i] based on linear OOA(3252, 174765, F32, 13, 13) (dual of [(174765, 13), 2271893, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3252, 1048591, F32, 13) (dual of [1048591, 1048539, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3252, 1048596, F32, 13) (dual of [1048596, 1048544, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,4]) [i] based on
- linear OA(3249, 1048577, F32, 13) (dual of [1048577, 1048528, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- 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]
- linear OA(323, 19, F32, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,32) or 19-cap in PG(2,32)), using
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- Reed–Solomon code RS(29,32) [i]
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- construction X applied to C([0,6]) ⊂ C([0,4]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3252, 1048596, F32, 13) (dual of [1048596, 1048544, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3252, 1048591, F32, 13) (dual of [1048591, 1048539, 14]-code), using
- net defined by OOA [i] based on linear OOA(3252, 174765, F32, 13, 13) (dual of [(174765, 13), 2271893, 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.