MinT - Information on Result #1801081

Information on Result #1801081

Digital (17, 22, 1179137)-net over F₁₆, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(16²², 1179137, F₁₆, 5) (dual of [1179137, 1179115, 6]-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁰, s, F₁₆, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
    - OA with only one run / dual of code without redundancy [i]
2. linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
3. linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
4. linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
5. linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
6. linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
7. linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
8. linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
9. linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
10. linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
11. linear OA(16⁰, 69905, F₁₆, 0) (dual of [69905, 69905, 1]-code) (see above)
12. linear OA(16¹, 69905, F₁₆, 1) (dual of [69905, 69904, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(16¹, s, F₁₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]
13. linear OA(16¹, 69905, F₁₆, 1) (dual of [69905, 69904, 2]-code) (see above)
14. linear OA(16¹, 69905, F₁₆, 1) (dual of [69905, 69904, 2]-code) (see above)
15. linear OA(16⁵, 69905, F₁₆, 2) (dual of [69905, 69900, 3]-code), using
  - Hamming code H(5,16) [i]
16. linear OA(16¹⁴, 130562, F₁₆, 5) (dual of [130562, 130548, 6]-code), using
  - trace code [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
    - a code by Danev and Olsson [i]

Mode: 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.