Information on Result #1234366
Digital (75, 89, 2527818)-net over F64, using generalized (u, u+v)-construction based on
- digital (7, 11, 131076)-net over F64, using
- net defined by OOA [i] based on linear OOA(6411, 131076, F64, 4, 4) (dual of [(131076, 4), 524293, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(6411, 131076, F64, 3, 4) (dual of [(131076, 3), 393217, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(6411, 262152, F64, 4) (dual of [262152, 262141, 5]-code), using
- construction X4 applied to Ce(3) ⊂ Ce(1) [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(644, 262144, F64, 2) (dual of [262144, 262140, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(647, 8, F64, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,64)), using
- dual of repetition code with length 8 [i]
- linear OA(641, 8, F64, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, 64, F64, 1) (dual of [64, 63, 2]-code), using
- Reed–Solomon code RS(63,64) [i]
- discarding factors / shortening the dual code based on linear OA(641, 64, F64, 1) (dual of [64, 63, 2]-code), using
- construction X4 applied to Ce(3) ⊂ Ce(1) [i] based on
- OA 2-folding and stacking [i] based on linear OA(6411, 262152, F64, 4) (dual of [262152, 262141, 5]-code), using
- appending kth column [i] based on linear OOA(6411, 131076, F64, 3, 4) (dual of [(131076, 3), 393217, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(6411, 131076, F64, 4, 4) (dual of [(131076, 4), 524293, 5]-NRT-code), using
- digital (18, 25, 1198371)-net over F64, using
- s-reduction based on digital (18, 25, 2796200)-net over F64, using
- net defined by OOA [i] based on linear OOA(6425, 2796200, F64, 7, 7) (dual of [(2796200, 7), 19573375, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(6425, 8388601, F64, 7) (dual of [8388601, 8388576, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(6425, large, F64, 7) (dual of [large, large−25, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6425, large, F64, 7) (dual of [large, large−25, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(6425, 8388601, F64, 7) (dual of [8388601, 8388576, 8]-code), using
- net defined by OOA [i] based on linear OOA(6425, 2796200, F64, 7, 7) (dual of [(2796200, 7), 19573375, 8]-NRT-code), using
- s-reduction based on digital (18, 25, 2796200)-net over F64, using
- digital (39, 53, 1198371)-net over F64, using
- net defined by OOA [i] based on linear OOA(6453, 1198371, F64, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(6453, 8388597, F64, 14) (dual of [8388597, 8388544, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(6453, large, F64, 14) (dual of [large, large−53, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(6453, large, F64, 14) (dual of [large, large−53, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(6453, 8388597, F64, 14) (dual of [8388597, 8388544, 15]-code), using
- net defined by OOA [i] based on linear OOA(6453, 1198371, F64, 14, 14) (dual of [(1198371, 14), 16777141, 15]-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.