Information on Result #1234833
Digital (72, 81, 4200942)-net over F9, using (u, u+v)-construction based on
- digital (11, 15, 6642)-net over F9, using
- base reduction for projective spaces (embedding PG(7,81) in PG(14,9)) for nets [i] based on digital (4, 8, 6642)-net over F81, using
- net defined by OOA [i] based on linear OOA(818, 6642, F81, 4, 4) (dual of [(6642, 4), 26560, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(818, 6642, F81, 3, 4) (dual of [(6642, 3), 19918, 5]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(810, s, F81, 3, 0) for arbitrarily large s, using
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
- linear OOA(811, 82, F81, 3, 1) (dual of [(82, 3), 245, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(811, s, F81, 3, 1) for arbitrarily large s, using
- appending 2 arbitrary columns [i] based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(811, s, F81, 3, 1) for arbitrarily large s, using
- linear OOA(811, 82, F81, 3, 1) (dual of [(82, 3), 245, 2]-NRT-code) (see above)
- linear OOA(812, 82, F81, 3, 2) (dual of [(82, 3), 244, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;244,81) [i]
- linear OOA(814, 82, F81, 3, 4) (dual of [(82, 3), 242, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;242,81) [i]
- linear OOA(810, 82, F81, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(818, 6642, F81, 3, 4) (dual of [(6642, 3), 19918, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(818, 6642, F81, 4, 4) (dual of [(6642, 4), 26560, 5]-NRT-code), using
- base reduction for projective spaces (embedding PG(7,81) in PG(14,9)) for nets [i] based on digital (4, 8, 6642)-net over F81, using
- digital (57, 66, 4194300)-net over F9, using
- net defined by OOA [i] based on linear OOA(966, 4194300, F9, 10, 9) (dual of [(4194300, 10), 41942934, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(966, 8388601, F9, 2, 9) (dual of [(8388601, 2), 16777136, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(966, 8388602, F9, 2, 9) (dual of [(8388602, 2), 16777138, 10]-NRT-code), using
- trace code [i] based on linear OOA(8133, 4194301, F81, 2, 9) (dual of [(4194301, 2), 8388569, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8133, 8388602, F81, 9) (dual of [8388602, 8388569, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(8133, large, F81, 9) (dual of [large, large−33, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, 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(8133, large, F81, 9) (dual of [large, large−33, 10]-code), using
- OOA 2-folding [i] based on linear OA(8133, 8388602, F81, 9) (dual of [8388602, 8388569, 10]-code), using
- trace code [i] based on linear OOA(8133, 4194301, F81, 2, 9) (dual of [(4194301, 2), 8388569, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(966, 8388602, F9, 2, 9) (dual of [(8388602, 2), 16777138, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(966, 8388601, F9, 2, 9) (dual of [(8388601, 2), 16777136, 10]-NRT-code), using
- net defined by OOA [i] based on linear OOA(966, 4194300, F9, 10, 9) (dual of [(4194300, 10), 41942934, 10]-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.