Information on Result #1184260
Digital (165, 181, 1048656)-net over F3, using net defined by OOA based on linear OOA(3181, 1048656, F3, 20, 16) (dual of [(1048656, 20), 20972939, 17]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(3181, 2097313, F3, 4, 16) (dual of [(2097313, 4), 8389071, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3181, 2097314, F3, 4, 16) (dual of [(2097314, 4), 8389075, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(330, 164, F3, 4, 8) (dual of [(164, 4), 626, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (22, 30, 164)-net over F3, using
- trace code for nets [i] based on digital (7, 15, 82)-net over F9, using
- base reduction for projective spaces (embedding PG(7,81) in PG(14,9)) for nets [i] based on digital (0, 8, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- base reduction for projective spaces (embedding PG(7,81) in PG(14,9)) for nets [i] based on digital (0, 8, 82)-net over F81, using
- trace code for nets [i] based on digital (7, 15, 82)-net over F9, using
- extracting embedded OOA [i] based on digital (22, 30, 164)-net over F3, using
- linear OOA(3151, 2097150, F3, 4, 16) (dual of [(2097150, 4), 8388449, 17]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3151, 8388600, F3, 16) (dual of [8388600, 8388449, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(3151, large, F3, 16) (dual of [large, large−151, 17]-code), using
- OOA 4-folding [i] based on linear OA(3151, 8388600, F3, 16) (dual of [8388600, 8388449, 17]-code), using
- linear OOA(330, 164, F3, 4, 8) (dual of [(164, 4), 626, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(3181, 2097314, F3, 4, 16) (dual of [(2097314, 4), 8389075, 17]-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.