Information on Result #1234174
Digital (79, 91, 6903166)-net over F64, using generalized (u, u+v)-construction based on
- digital (0, 0, 87382)-net over F64, using
- s-reduction based on digital (0, 0, s)-net over F64 for arbitrarily large s, using
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 0, 87382)-net over F64 (see above)
- digital (0, 1, 87382)-net over F64, using
- s-reduction based on digital (0, 1, s)-net over F64 for arbitrarily large s, using
- digital (0, 1, 87382)-net over F64 (see above)
- digital (0, 1, 87382)-net over F64 (see above)
- digital (0, 1, 87382)-net over F64 (see above)
- digital (0, 1, 87382)-net over F64 (see above)
- digital (0, 1, 87382)-net over F64 (see above)
- digital (2, 4, 87382)-net over F64, using
- s-reduction based on digital (2, 4, 266305)-net over F64, using
- digital (2, 4, 87382)-net over F64 (see above)
- digital (3, 6, 87382)-net over F64, using
- s-reduction based on digital (3, 6, 270402)-net over F64, using
- net defined by OOA [i] based on linear OOA(646, 270402, F64, 3, 3) (dual of [(270402, 3), 811200, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(646, 270402, F64, 2, 3) (dual of [(270402, 2), 540798, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(646, 270402, F64, 3, 3) (dual of [(270402, 3), 811200, 4]-NRT-code), using
- s-reduction based on digital (3, 6, 270402)-net over F64, using
- digital (6, 10, 87382)-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 (10, 16, 87382)-net over F64, using
- net defined by OOA [i] based on linear OOA(6416, 87382, F64, 6, 6) (dual of [(87382, 6), 524276, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(6416, 262146, F64, 6) (dual of [262146, 262130, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(6416, 262147, F64, 6) (dual of [262147, 262131, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(6416, 262144, F64, 6) (dual of [262144, 262128, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(6413, 262144, F64, 5) (dual of [262144, 262131, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 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(6416, 262147, F64, 6) (dual of [262147, 262131, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(6416, 262146, F64, 6) (dual of [262146, 262130, 7]-code), using
- net defined by OOA [i] based on linear OOA(6416, 87382, F64, 6, 6) (dual of [(87382, 6), 524276, 7]-NRT-code), using
- digital (33, 45, 1398100)-net over F64, using
- net defined by OOA [i] based on linear OOA(6445, 1398100, F64, 12, 12) (dual of [(1398100, 12), 16777155, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(6445, 8388600, F64, 12) (dual of [8388600, 8388555, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(6445, large, F64, 12) (dual of [large, large−45, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(6445, large, F64, 12) (dual of [large, large−45, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(6445, 8388600, F64, 12) (dual of [8388600, 8388555, 13]-code), using
- net defined by OOA [i] based on linear OOA(6445, 1398100, F64, 12, 12) (dual of [(1398100, 12), 16777155, 13]-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.