Information on Result #1234188
Digital (39, 47, 4194496)-net over F64, using generalized (u, u+v)-construction based on
- digital (0, 0, 65539)-net over F64, using
- s-reduction based on digital (0, 0, s)-net over F64 for arbitrarily large s, using
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 0, 65539)-net over F64 (see above)
- digital (0, 1, 65539)-net over F64, using
- s-reduction based on digital (0, 1, s)-net over F64 for arbitrarily large s, using
- digital (0, 1, 65539)-net over F64 (see above)
- digital (0, 1, 65539)-net over F64 (see above)
- digital (0, 1, 65539)-net over F64 (see above)
- digital (2, 4, 65539)-net over F64, using
- s-reduction based on digital (2, 4, 266305)-net over F64, using
- digital (2, 4, 65539)-net over F64 (see above)
- digital (6, 10, 65539)-net over F64, using
- s-reduction based on digital (6, 10, 131073)-net over F64, using
- net defined by OOA [i] based on linear OOA(6410, 131073, F64, 4, 4) (dual of [(131073, 4), 524282, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(6410, 131073, F64, 3, 4) (dual of [(131073, 3), 393209, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(6410, 262146, F64, 4) (dual of [262146, 262136, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(6410, 262147, F64, 4) (dual of [262147, 262137, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(6410, 262144, F64, 4) (dual of [262144, 262134, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(647, 262144, F64, 3) (dual of [262144, 262137, 4]-code or 262144-cap in PG(6,64)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(6410, 262147, F64, 4) (dual of [262147, 262137, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(6410, 262146, F64, 4) (dual of [262146, 262136, 5]-code), using
- appending kth column [i] based on linear OOA(6410, 131073, F64, 3, 4) (dual of [(131073, 3), 393209, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(6410, 131073, F64, 4, 4) (dual of [(131073, 4), 524282, 5]-NRT-code), using
- s-reduction based on digital (6, 10, 131073)-net over F64, using
- digital (17, 25, 65539)-net over F64, using
- net defined by OOA [i] based on linear OOA(6425, 65539, F64, 8, 8) (dual of [(65539, 8), 524287, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(6425, 262156, F64, 8) (dual of [262156, 262131, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(6425, 262159, F64, 8) (dual of [262159, 262134, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(3) [i] based on
- linear OA(6422, 262144, F64, 8) (dual of [262144, 262122, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(6410, 262144, F64, 4) (dual of [262144, 262134, 5]-code) (see above)
- linear OA(643, 15, F64, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,64) or 15-cap in PG(2,64)), using
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- Reed–Solomon code RS(61,64) [i]
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- construction X applied to Ce(7) ⊂ Ce(3) [i] based on
- discarding factors / shortening the dual code based on linear OA(6425, 262159, F64, 8) (dual of [262159, 262134, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(6425, 262156, F64, 8) (dual of [262156, 262131, 9]-code), using
- net defined by OOA [i] based on linear OOA(6425, 65539, F64, 8, 8) (dual of [(65539, 8), 524287, 9]-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.