Information on Result #1184772
Digital (231, 250, 1062900)-net over F3, using net defined by OOA based on linear OOA(3250, 1062900, F3, 21, 19) (dual of [(1062900, 21), 22320650, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(3250, 3188701, F3, 3, 19) (dual of [(3188701, 3), 9565853, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3250, 3188702, F3, 3, 19) (dual of [(3188702, 3), 9565856, 20]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(324, 56, F3, 3, 9) (dual of [(56, 3), 144, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (15, 24, 56)-net over F3, using
- trace code for nets [i] based on digital (3, 12, 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, 12, 28)-net over F9, using
- extracting embedded OOA [i] based on digital (15, 24, 56)-net over F3, using
- linear OOA(3226, 3188646, F3, 3, 19) (dual of [(3188646, 3), 9565712, 20]-NRT-code), using
- trace code [i] based on linear OOA(9113, 1594323, F9, 3, 19) (dual of [(1594323, 3), 4782856, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(9113, 4782969, F9, 19) (dual of [4782969, 4782856, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OOA 3-folding [i] based on linear OA(9113, 4782969, F9, 19) (dual of [4782969, 4782856, 20]-code), using
- trace code [i] based on linear OOA(9113, 1594323, F9, 3, 19) (dual of [(1594323, 3), 4782856, 20]-NRT-code), using
- linear OOA(324, 56, F3, 3, 9) (dual of [(56, 3), 144, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(3250, 3188702, F3, 3, 19) (dual of [(3188702, 3), 9565856, 20]-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.