Information on Result #1226814
Digital (47, 56, 4456446)-net over F64, using (u, u+v)-construction based on
- digital (9, 13, 4194301)-net over F64, using
- net defined by OOA [i] based on linear OOA(6413, 4194301, F64, 4, 4) (dual of [(4194301, 4), 16777191, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(6413, 4194301, F64, 3, 4) (dual of [(4194301, 3), 12582890, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(6413, 8388602, F64, 4) (dual of [8388602, 8388589, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(6413, large, F64, 4) (dual of [large, large−13, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(6413, large, F64, 4) (dual of [large, large−13, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(6413, 8388602, F64, 4) (dual of [8388602, 8388589, 5]-code), using
- appending kth column [i] based on linear OOA(6413, 4194301, F64, 3, 4) (dual of [(4194301, 3), 12582890, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(6413, 4194301, F64, 4, 4) (dual of [(4194301, 4), 16777191, 5]-NRT-code), using
- digital (34, 43, 2228223)-net over F64, using
- (u, u+v)-construction [i] 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
- digital (24, 33, 2097150)-net over F64, using
- net defined by OOA [i] based on linear OOA(6433, 2097150, F64, 9, 9) (dual of [(2097150, 9), 18874317, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(6433, 8388601, F64, 9) (dual of [8388601, 8388568, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(6433, large, F64, 9) (dual of [large, large−33, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6433, large, F64, 9) (dual of [large, large−33, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(6433, 8388601, F64, 9) (dual of [8388601, 8388568, 10]-code), using
- net defined by OOA [i] based on linear OOA(6433, 2097150, F64, 9, 9) (dual of [(2097150, 9), 18874317, 10]-NRT-code), using
- digital (6, 10, 131073)-net over F64, using
- (u, u+v)-construction [i] based on
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.