Information on Result #1234830
Digital (65, 73, 4198460)-net over F8, using (u, u+v)-construction based on
- digital (11, 15, 4160)-net over F8, using
- base reduction for projective spaces (embedding PG(7,64) in PG(14,8)) for nets [i] based on digital (4, 8, 4160)-net over F64, using
- net defined by OOA [i] based on linear OOA(648, 4160, F64, 4, 4) (dual of [(4160, 4), 16632, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(648, 4160, F64, 3, 4) (dual of [(4160, 3), 12472, 5]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(640, s, F64, 3, 0) for arbitrarily large s, using
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
- linear OOA(641, 65, F64, 3, 1) (dual of [(65, 3), 194, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(641, s, F64, 3, 1) for arbitrarily large s, using
- appending 2 arbitrary columns [i] based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(641, s, F64, 3, 1) for arbitrarily large s, using
- linear OOA(641, 65, F64, 3, 1) (dual of [(65, 3), 194, 2]-NRT-code) (see above)
- linear OOA(642, 65, F64, 3, 2) (dual of [(65, 3), 193, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;193,64) [i]
- linear OOA(644, 65, F64, 3, 4) (dual of [(65, 3), 191, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;191,64) [i]
- linear OOA(640, 65, F64, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(648, 4160, F64, 3, 4) (dual of [(4160, 3), 12472, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(648, 4160, F64, 4, 4) (dual of [(4160, 4), 16632, 5]-NRT-code), using
- base reduction for projective spaces (embedding PG(7,64) in PG(14,8)) for nets [i] based on digital (4, 8, 4160)-net over F64, using
- digital (50, 58, 4194300)-net over F8, using
- net defined by OOA [i] based on linear OOA(858, 4194300, F8, 10, 8) (dual of [(4194300, 10), 41942942, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(858, 8388601, F8, 2, 8) (dual of [(8388601, 2), 16777144, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(858, 8388602, F8, 2, 8) (dual of [(8388602, 2), 16777146, 9]-NRT-code), using
- trace code [i] based on linear OOA(6429, 4194301, F64, 2, 8) (dual of [(4194301, 2), 8388573, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6429, 8388602, F64, 8) (dual of [8388602, 8388573, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- OOA 2-folding [i] based on linear OA(6429, 8388602, F64, 8) (dual of [8388602, 8388573, 9]-code), using
- trace code [i] based on linear OOA(6429, 4194301, F64, 2, 8) (dual of [(4194301, 2), 8388573, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(858, 8388602, F8, 2, 8) (dual of [(8388602, 2), 16777146, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(858, 8388601, F8, 2, 8) (dual of [(8388601, 2), 16777144, 9]-NRT-code), using
- net defined by OOA [i] based on linear OOA(858, 4194300, F8, 10, 8) (dual of [(4194300, 10), 41942942, 9]-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.