MinT - Information on Result #3178070

Information on Result #3178070

Digital (46, 52, large)-net over F₄₉, using 2 times m-reduction based on digital (46, 54, large)-net over F₄₉, using

generalized (u,Â u+v)-construction [i] based on
1. digital (0, 0, 120100)-net over F₄₉, using
  - s-reduction based on digital (0, 0, s)-net over F₄₉ for arbitrarily large s, using
    - arbitrary set of 49⁰ points [i]
2. digital (0, 0, 120100)-net over F₄₉ (see above)
3. digital (0, 0, 120100)-net over F₄₉ (see above)
4. digital (0, 0, 120100)-net over F₄₉ (see above)
5. digital (0, 0, 120100)-net over F₄₉ (see above)
6. digital (0, 0, 120100)-net over F₄₉ (see above)
7. digital (0, 0, 120100)-net over F₄₉ (see above)
8. digital (0, 0, 120100)-net over F₄₉ (see above)
9. digital (0, 0, 120100)-net over F₄₉ (see above)
10. digital (0, 0, 120100)-net over F₄₉ (see above)
11. digital (0, 0, 120100)-net over F₄₉ (see above)
12. digital (0, 0, 120100)-net over F₄₉ (see above)
13. digital (0, 0, 120100)-net over F₄₉ (see above)
14. digital (0, 0, 120100)-net over F₄₉ (see above)
15. digital (0, 0, 120100)-net over F₄₉ (see above)
16. digital (0, 0, 120100)-net over F₄₉ (see above)
17. digital (0, 0, 120100)-net over F₄₉ (see above)
18. digital (0, 0, 120100)-net over F₄₉ (see above)
19. digital (0, 0, 120100)-net over F₄₉ (see above)
20. digital (0, 0, 120100)-net over F₄₉ (see above)
21. digital (0, 0, 120100)-net over F₄₉ (see above)
22. digital (0, 0, 120100)-net over F₄₉ (see above)
23. digital (0, 0, 120100)-net over F₄₉ (see above)
24. digital (0, 0, 120100)-net over F₄₉ (see above)
25. digital (0, 0, 120100)-net over F₄₉ (see above)
26. digital (0, 0, 120100)-net over F₄₉ (see above)
27. digital (0, 0, 120100)-net over F₄₉ (see above)
28. digital (0, 0, 120100)-net over F₄₉ (see above)
29. digital (0, 0, 120100)-net over F₄₉ (see above)
30. digital (0, 0, 120100)-net over F₄₉ (see above)
31. digital (0, 0, 120100)-net over F₄₉ (see above)
32. digital (0, 0, 120100)-net over F₄₉ (see above)
33. digital (0, 0, 120100)-net over F₄₉ (see above)
34. digital (0, 0, 120100)-net over F₄₉ (see above)
35. digital (0, 0, 120100)-net over F₄₉ (see above)
36. digital (0, 0, 120100)-net over F₄₉ (see above)
37. digital (0, 0, 120100)-net over F₄₉ (see above)
38. digital (0, 0, 120100)-net over F₄₉ (see above)
39. digital (0, 0, 120100)-net over F₄₉ (see above)
40. digital (0, 0, 120100)-net over F₄₉ (see above)
41. digital (0, 0, 120100)-net over F₄₉ (see above)
42. digital (0, 1, 120100)-net over F₄₉, using
  - s-reduction based on digital (0, 1, s)-net over F₄₉ for arbitrarily large s, using
    - construction for strength kÂ =Â 1 [i]
43. digital (0, 1, 120100)-net over F₄₉ (see above)
44. digital (0, 1, 120100)-net over F₄₉ (see above)
45. digital (0, 1, 120100)-net over F₄₉ (see above)
46. digital (2, 4, 120100)-net over F₄₉, using
  - kÂ =Â 2 construction [i]
47. digital (2, 4, 120100)-net over F₄₉ (see above)
48. digital (9, 13, 1441201)-net over F₄₉, using
  - s-reduction based on digital (9, 13, 2882402)-net over F₄₉, using
    - net defined by OOA [i] based on linear OOA(49¹³, 2882402, F₄₉, 4, 4) (dual of [(2882402, 4), 11529595, 5]-NRT-code), using
      - appending kth column [i] based on linear OOA(49¹³, 2882402, F₄₉, 3, 4) (dual of [(2882402, 3), 8647193, 5]-NRT-code), using
        OA 2-folding and stacking [i] based on linear OA(49¹³, 5764804, F₄₉, 4) (dual of [5764804, 5764791, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(49¹³, 5764805, F₄₉, 4) (dual of [5764805, 5764792, 5]-code), using
        constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
        linear OA(49¹³, 5764801, F₄₉, 4) (dual of [5764801, 5764788, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(49⁹, 5764801, F₄₉, 3) (dual of [5764801, 5764792, 4]-code or 5764801-cap in PG(8,49)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
        linear OA(49⁰, 4, F₄₉, 0) (dual of [4, 4, 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]
49. digital (21, 29, 1441201)-net over F₄₉, using
  - net defined by OOA [i] based on linear OOA(49²⁹, 1441201, F₄₉, 8, 8) (dual of [(1441201, 8), 11529579, 9]-NRT-code), using
    - OA 4-folding and stacking [i] based on linear OA(49²⁹, 5764804, F₄₉, 8) (dual of [5764804, 5764775, 9]-code), using
      - discarding factors / shortening the dual code based on linear OA(49²⁹, 5764805, F₄₉, 8) (dual of [5764805, 5764776, 9]-code), using
        constructionÂ X applied to C_e(7) âŠ‚ C_e(6) [i] based on
        linear OA(49²⁹, 5764801, F₄₉, 8) (dual of [5764801, 5764772, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
        linear OA(49²⁵, 5764801, F₄₉, 7) (dual of [5764801, 5764776, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(49⁰, 4, F₄₉, 0) (dual of [4, 4, 1]-code) (see above)

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Digital (47, 52, large)-net over F₄₉	[i]	t-Expansion
2	Digital (48, 52, large)-net over F₄₉	[i]
3	Digital (49, 52, large)-net over F₄₉	[i]