Information on Result #1210621
Digital (174, 191, 2097159)-net over F4, using (u, u+v)-construction based on
- digital (1, 9, 9)-net over F4, using
- net from sequence [i] based on digital (1, 8)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- the Hermitian function field over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- net from sequence [i] based on digital (1, 8)-sequence over F4, using
- digital (165, 182, 2097150)-net over F4, using
- net defined by OOA [i] based on linear OOA(4182, 2097150, F4, 18, 17) (dual of [(2097150, 18), 37748518, 18]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(4182, 8388601, F4, 2, 17) (dual of [(8388601, 2), 16777020, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4182, 8388602, F4, 2, 17) (dual of [(8388602, 2), 16777022, 18]-NRT-code), using
- trace code [i] based on linear OOA(1691, 4194301, F16, 2, 17) (dual of [(4194301, 2), 8388511, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(1691, 8388602, F16, 17) (dual of [8388602, 8388511, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(1691, large, F16, 17) (dual of [large, large−91, 18]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(1691, large, F16, 17) (dual of [large, large−91, 18]-code), using
- OOA 2-folding [i] based on linear OA(1691, 8388602, F16, 17) (dual of [8388602, 8388511, 18]-code), using
- trace code [i] based on linear OOA(1691, 4194301, F16, 2, 17) (dual of [(4194301, 2), 8388511, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4182, 8388602, F4, 2, 17) (dual of [(8388602, 2), 16777022, 18]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(4182, 8388601, F4, 2, 17) (dual of [(8388601, 2), 16777020, 18]-NRT-code), using
- net defined by OOA [i] based on linear OOA(4182, 2097150, F4, 18, 17) (dual of [(2097150, 18), 37748518, 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.