MinT - Information on Result #1224672

Information on Result #1224672

Digital (52, 62, 1711511)-net over F₃₂, using (u,Â u+v)-construction based on

digital (11, 16, 33791)-net over F₃₂, using
- net defined by OOA [i] based on linear OOA(32¹⁶, 33791, F₃₂, 6, 5) (dual of [(33791, 6), 202730, 6]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(32¹⁶, 33792, F₃₂, 2, 5) (dual of [(33792, 2), 67568, 6]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(32⁰, s, F₃₂, 2, 0) for arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
      2. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      3. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      4. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      5. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      6. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      7. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      8. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      9. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      10. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      11. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      12. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      13. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      14. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      15. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      16. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      17. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      18. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      19. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      20. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      21. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      22. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      23. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      24. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      25. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      26. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      27. linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
      28. linear OOA(32¹, 1056, F₃₂, 2, 1) (dual of [(1056, 2), 2111, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(32¹, s, F₃₂, 2, 1) for arbitrarily large s, using
        appending 1 arbitrary column [i] based on linear OA(32¹, s, F₃₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      29. linear OOA(32¹, 1056, F₃₂, 2, 1) (dual of [(1056, 2), 2111, 2]-NRT-code) (see above)
      30. linear OOA(32¹, 1056, F₃₂, 2, 1) (dual of [(1056, 2), 2111, 2]-NRT-code) (see above)
      31. linear OOA(32³, 1056, F₃₂, 2, 2) (dual of [(1056, 2), 2109, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(32³, 1057, F₃₂, 2, 2) (dual of [(1057, 2), 2111, 3]-NRT-code), using
        appending kth column [i] based on linear OA(32³, 1057, F₃₂, 2) (dual of [1057, 1054, 3]-code), using
        Hamming code H(3,32) [i]
      32. linear OOA(32¹⁰, 1056, F₃₂, 2, 5) (dual of [(1056, 2), 2102, 6]-NRT-code), using
        generalized (u,Â u+v)-construction [i] based on
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(32⁰, s, F₃₂, 2, 0) for arbitrarily large s (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
        linear OOA(32¹, 33, F₃₂, 2, 1) (dual of [(33, 2), 65, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(32¹, s, F₃₂, 2, 1) for arbitrarily large s (see above)
        linear OOA(32¹, 33, F₃₂, 2, 1) (dual of [(33, 2), 65, 2]-NRT-code) (see above)
        linear OOA(32¹, 33, F₃₂, 2, 1) (dual of [(33, 2), 65, 2]-NRT-code) (see above)
        linear OOA(32², 33, F₃₂, 2, 2) (dual of [(33, 2), 64, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;64,32) [i]
        linear OOA(32⁵, 33, F₃₂, 2, 5) (dual of [(33, 2), 61, 6]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;61,32) [i]
digital (36, 46, 1677720)-net over F₃₂, using
- net defined by OOA [i] based on linear OOA(32⁴⁶, 1677720, F₃₂, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
  - OA 5-folding and stacking [i] based on linear OA(32⁴⁶, 8388600, F₃₂, 10) (dual of [8388600, 8388554, 11]-code), using
    - discarding factors / shortening the dual code based on linear OA(32⁴⁶, large, F₃₂, 10) (dual of [large, large−46, 11]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 33554431Â = 32⁵âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

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

The following results depend on this result:

	Result		This result only	Method
1	Digital (73, 83, 3423022)-net over F₃₂	[i]		(u,Â u+v)-Construction for Nets