Information on Result #1229732
Digital (97, 109, 1921809)-net over F7, using (u, u+v)-construction based on
- digital (13, 19, 208)-net over F7, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 8)-net over F7, using
- digital (2, 5, 100)-net over F7, using
- s-reduction based on digital (2, 5, 132)-net over F7, using
- net defined by OOA [i] based on linear OOA(75, 132, F7, 3, 3) (dual of [(132, 3), 391, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(75, 132, F7, 2, 3) (dual of [(132, 2), 259, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(75, 132, F7, 3, 3) (dual of [(132, 3), 391, 4]-NRT-code), using
- s-reduction based on digital (2, 5, 132)-net over F7, using
- digital (6, 12, 100)-net over F7, using
- trace code for nets [i] based on digital (0, 6, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- trace code for nets [i] based on digital (0, 6, 50)-net over F49, using
- generalized (u, u+v)-construction [i] based on
- digital (78, 90, 1921601)-net over F7, using
- net defined by OOA [i] based on linear OOA(790, 1921601, F7, 14, 12) (dual of [(1921601, 14), 26902324, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(790, 5764804, F7, 2, 12) (dual of [(5764804, 2), 11529518, 13]-NRT-code), using
- trace code [i] based on linear OOA(4945, 2882402, F49, 2, 12) (dual of [(2882402, 2), 5764759, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4945, 5764804, F49, 12) (dual of [5764804, 5764759, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(4945, 5764805, F49, 12) (dual of [5764805, 5764760, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(4945, 5764801, F49, 12) (dual of [5764801, 5764756, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(4941, 5764801, F49, 11) (dual of [5764801, 5764760, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(4945, 5764805, F49, 12) (dual of [5764805, 5764760, 13]-code), using
- OOA 2-folding [i] based on linear OA(4945, 5764804, F49, 12) (dual of [5764804, 5764759, 13]-code), using
- trace code [i] based on linear OOA(4945, 2882402, F49, 2, 12) (dual of [(2882402, 2), 5764759, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(790, 5764804, F7, 2, 12) (dual of [(5764804, 2), 11529518, 13]-NRT-code), using
- net defined by OOA [i] based on linear OOA(790, 1921601, F7, 14, 12) (dual of [(1921601, 14), 26902324, 13]-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.