Information on Result #1232995
Digital (73, 84, 6711008)-net over F32, using generalized (u, u+v)-construction based on
- digital (0, 0, 209719)-net over F32, using
- s-reduction based on digital (0, 0, s)-net over F32 for arbitrarily large s, using
- digital (0, 0, 209719)-net over F32 (see above)
- digital (0, 0, 209719)-net over F32 (see above)
- digital (0, 0, 209719)-net over F32 (see above)
- digital (0, 0, 209719)-net over F32 (see above)
- digital (0, 0, 209719)-net over F32 (see above)
- digital (0, 0, 209719)-net over F32 (see above)
- digital (0, 0, 209719)-net over F32 (see above)
- digital (0, 0, 209719)-net over F32 (see above)
- digital (0, 0, 209719)-net over F32 (see above)
- digital (0, 0, 209719)-net over F32 (see above)
- digital (0, 0, 209719)-net over F32 (see above)
- digital (0, 0, 209719)-net over F32 (see above)
- digital (0, 0, 209719)-net over F32 (see above)
- digital (0, 0, 209719)-net over F32 (see above)
- digital (0, 0, 209719)-net over F32 (see above)
- digital (0, 0, 209719)-net over F32 (see above)
- digital (0, 0, 209719)-net over F32 (see above)
- digital (0, 0, 209719)-net over F32 (see above)
- digital (0, 0, 209719)-net over F32 (see above)
- digital (0, 0, 209719)-net over F32 (see above)
- digital (0, 1, 209719)-net over F32, using
- s-reduction based on digital (0, 1, s)-net over F32 for arbitrarily large s, using
- digital (0, 1, 209719)-net over F32 (see above)
- digital (0, 1, 209719)-net over F32 (see above)
- digital (0, 1, 209719)-net over F32 (see above)
- digital (0, 1, 209719)-net over F32 (see above)
- digital (0, 1, 209719)-net over F32 (see above)
- digital (3, 5, 209719)-net over F32, using
- s-reduction based on digital (3, 5, 1082401)-net over F32, using
- digital (3, 5, 209719)-net over F32 (see above)
- digital (4, 7, 209719)-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 (12, 17, 209719)-net over F32, using
- s-reduction based on digital (12, 17, 524289)-net over F32, using
- net defined by OOA [i] based on linear OOA(3217, 524289, F32, 5, 5) (dual of [(524289, 5), 2621428, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(3217, 1048579, F32, 5) (dual of [1048579, 1048562, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(3217, 1048580, F32, 5) (dual of [1048580, 1048563, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- 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(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(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(4) ⊂ Ce(3) [i] based on
- discarding factors / shortening the dual code based on linear OA(3217, 1048580, F32, 5) (dual of [1048580, 1048563, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(3217, 1048579, F32, 5) (dual of [1048579, 1048562, 6]-code), using
- net defined by OOA [i] based on linear OOA(3217, 524289, F32, 5, 5) (dual of [(524289, 5), 2621428, 6]-NRT-code), using
- s-reduction based on digital (12, 17, 524289)-net over F32, using
- digital (33, 44, 209719)-net over F32, using
- net defined by OOA [i] based on linear OOA(3244, 209719, F32, 11, 11) (dual of [(209719, 11), 2306865, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(3244, 1048596, F32, 11) (dual of [1048596, 1048552, 12]-code), using
- construction X applied to C([0,5]) ⊂ C([0,3]) [i] based on
- linear OA(3241, 1048577, F32, 11) (dual of [1048577, 1048536, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(3225, 1048577, F32, 7) (dual of [1048577, 1048552, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (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([0,5]) ⊂ C([0,3]) [i] based on
- OOA 5-folding and stacking with additional row [i] based on linear OA(3244, 1048596, F32, 11) (dual of [1048596, 1048552, 12]-code), using
- net defined by OOA [i] based on linear OOA(3244, 209719, F32, 11, 11) (dual of [(209719, 11), 2306865, 12]-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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (74, 85, 6711008)-net over F32 | [i] | Net Duplication | |