MinT - Information on Result #1810280

Information on Result #1810280

Digital (10, 15, 117747)-net over F₄₉, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(49¹⁵, 117747, F₄₉, 5) (dual of [117747, 117732, 6]-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(49⁰, s, F₄₉, 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(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
3. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
4. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
5. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
6. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
7. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
8. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
9. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
10. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
11. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
12. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
13. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
14. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
15. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
16. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
17. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
18. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
19. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
20. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
21. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
22. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
23. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
24. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
25. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
26. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
27. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
28. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
29. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
30. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
31. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
32. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
33. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
34. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
35. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
36. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
37. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
38. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
39. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
40. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
41. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
42. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
43. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
44. linear OA(49⁰, 2403, F₄₉, 0) (dual of [2403, 2403, 1]-code) (see above)
45. linear OA(49¹, 2403, F₄₉, 1) (dual of [2403, 2402, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(49¹, s, F₄₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]
46. linear OA(49¹, 2403, F₄₉, 1) (dual of [2403, 2402, 2]-code) (see above)
47. linear OA(49¹, 2403, F₄₉, 1) (dual of [2403, 2402, 2]-code) (see above)
48. linear OA(49³, 2403, F₄₉, 2) (dual of [2403, 2400, 3]-code), using
  - discarding factors / shortening the dual code based on linear OA(49³, 2451, F₄₉, 2) (dual of [2451, 2448, 3]-code), using
    - Hamming code H(3,49) [i]
49. linear OA(49⁹, 2403, F₄₉, 5) (dual of [2403, 2394, 6]-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OA(49², 50, F₄₉, 2) (dual of [50, 48, 3]-code or 50-arc in PG(1,49)), using
      - extended Reedâ€“Solomon code RS_e(48,49) [i]
      - Hamming code H(2,49) [i]
      - algebraic-geometric code AG(F, Q+22P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50, using the rational function field F₄₉(x) [i]
    2. linear OA(49⁷, 2353, F₄₉, 5) (dual of [2353, 2346, 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.