Information on Result #1229841
Digital (157, 171, 4795708)-net over F8, using generalized (u, u+v)-construction based on
- digital (2, 5, 208)-net over F8, using
- net defined by OOA [i] based on linear OOA(85, 208, F8, 3, 3) (dual of [(208, 3), 619, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(85, 208, F8, 2, 3) (dual of [(208, 2), 411, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(85, 208, F8, 3, 3) (dual of [(208, 3), 619, 4]-NRT-code), using
- digital (7, 11, 2016)-net over F8, using
- net defined by OOA [i] based on linear OOA(811, 2016, F8, 4, 4) (dual of [(2016, 4), 8053, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(811, 2016, F8, 3, 4) (dual of [(2016, 3), 6037, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(811, 4032, F8, 4) (dual of [4032, 4021, 5]-code), using
- base reduction for projective spaces (embedding PG(5,64) in PG(10,8)) [i] based on linear OA(646, 4032, F64, 4) (dual of [4032, 4026, 5]-code), using
- 1 times truncation [i] based on linear OA(647, 4033, F64, 5) (dual of [4033, 4026, 6]-code), using
- base reduction for projective spaces (embedding PG(5,64) in PG(10,8)) [i] based on linear OA(646, 4032, F64, 4) (dual of [4032, 4026, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(811, 4032, F8, 4) (dual of [4032, 4021, 5]-code), using
- appending kth column [i] based on linear OOA(811, 2016, F8, 3, 4) (dual of [(2016, 3), 6037, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(811, 2016, F8, 4, 4) (dual of [(2016, 4), 8053, 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.