Information on Result #1229766
Digital (153, 167, 4793549)-net over F8, using generalized (u, u+v)-construction based on
- digital (0, 2, 9)-net over F8, using
- digital (1, 4, 28)-net over F8, using
- s-reduction based on digital (1, 4, 65)-net over F8, using
- net defined by OOA [i] based on linear OOA(84, 65, F8, 3, 3) (dual of [(65, 3), 191, 4]-NRT-code), using
- s-reduction based on digital (1, 4, 65)-net over F8, using
- digital (2, 6, 28)-net over F8, using
- net defined by OOA [i] based on linear OOA(86, 28, F8, 4, 4) (dual of [(28, 4), 106, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(86, 28, F8, 3, 4) (dual of [(28, 3), 78, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- 1 times truncation [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- appending kth column [i] based on linear OOA(86, 28, F8, 3, 4) (dual of [(28, 3), 78, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(86, 28, F8, 4, 4) (dual of [(28, 4), 106, 5]-NRT-code), using
- digital (42, 49, 2396742)-net over F8, using
- s-reduction based on digital (42, 49, 2796200)-net over F8, using
- net defined by OOA [i] based on linear OOA(849, 2796200, F8, 7, 7) (dual of [(2796200, 7), 19573351, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(849, 8388601, F8, 7) (dual of [8388601, 8388552, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(849, large, F8, 7) (dual of [large, large−49, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 816−1, 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(849, large, F8, 7) (dual of [large, large−49, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(849, 8388601, F8, 7) (dual of [8388601, 8388552, 8]-code), using
- net defined by OOA [i] based on linear OOA(849, 2796200, F8, 7, 7) (dual of [(2796200, 7), 19573351, 8]-NRT-code), using
- s-reduction based on digital (42, 49, 2796200)-net over F8, using
- digital (92, 106, 2396742)-net over F8, using
- trace code for nets [i] based on 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
- trace code for nets [i] based on digital (39, 53, 1198371)-net over F64, 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.