Information on Result #1184416
Digital (171, 188, 1048602)-net over F3, using net defined by OOA based on linear OOA(3188, 1048602, F3, 20, 17) (dual of [(1048602, 20), 20971852, 18]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(3188, 2097205, F3, 4, 17) (dual of [(2097205, 4), 8388632, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3188, 2097206, F3, 4, 17) (dual of [(2097206, 4), 8388636, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(322, 56, F3, 4, 8) (dual of [(56, 4), 202, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (14, 22, 56)-net over F3, using
- trace code for nets [i] based on digital (3, 11, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- trace code for nets [i] based on digital (3, 11, 28)-net over F9, using
- extracting embedded OOA [i] based on digital (14, 22, 56)-net over F3, using
- linear OOA(3166, 2097150, F3, 4, 17) (dual of [(2097150, 4), 8388434, 18]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3166, 8388600, F3, 17) (dual of [8388600, 8388434, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3166, large, F3, 17) (dual of [large, large−166, 18]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(3166, large, F3, 17) (dual of [large, large−166, 18]-code), using
- OOA 4-folding [i] based on linear OA(3166, 8388600, F3, 17) (dual of [8388600, 8388434, 18]-code), using
- linear OOA(322, 56, F3, 4, 8) (dual of [(56, 4), 202, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(3188, 2097206, F3, 4, 17) (dual of [(2097206, 4), 8388636, 18]-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.