Information on Result #1217352
Digital (97, 108, 3886883)-net over F9, using (u, u+v)-construction based on
- digital (21, 26, 531443)-net over F9, using
- net defined by OOA [i] based on linear OOA(926, 531443, F9, 5, 5) (dual of [(531443, 5), 2657189, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(926, 1062887, F9, 5) (dual of [1062887, 1062861, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(926, 1062888, F9, 5) (dual of [1062888, 1062862, 6]-code), using
- trace code [i] based on linear OA(8113, 531444, F81, 5) (dual of [531444, 531431, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(8113, 531441, F81, 5) (dual of [531441, 531428, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(8110, 531441, F81, 4) (dual of [531441, 531431, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- trace code [i] based on linear OA(8113, 531444, F81, 5) (dual of [531444, 531431, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(926, 1062888, F9, 5) (dual of [1062888, 1062862, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(926, 1062887, F9, 5) (dual of [1062887, 1062861, 6]-code), using
- net defined by OOA [i] based on linear OOA(926, 531443, F9, 5, 5) (dual of [(531443, 5), 2657189, 6]-NRT-code), using
- digital (71, 82, 3355440)-net over F9, using
- trace code for nets [i] based on digital (30, 41, 1677720)-net over F81, using
- net defined by OOA [i] based on linear OOA(8141, 1677720, F81, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(8141, 8388601, F81, 11) (dual of [8388601, 8388560, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(8141, large, F81, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8141, large, F81, 11) (dual of [large, large−41, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(8141, 8388601, F81, 11) (dual of [8388601, 8388560, 12]-code), using
- net defined by OOA [i] based on linear OOA(8141, 1677720, F81, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- trace code for nets [i] based on digital (30, 41, 1677720)-net over F81, 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.