MinT - Information on Result #1195836

Information on Result #1195836

Digital (11, 16, 16249)-net over F₂₅, using net defined by OOA based on linear OOA(25¹⁶, 16249, F₂₅, 6, 5) (dual of [(16249, 6), 97478, 6]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(25¹⁶, 16250, F₂₅, 2, 5) (dual of [(16250, 2), 32484, 6]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(25⁰, 650, F₂₅, 2, 0) (dual of [(650, 2), 1300, 1]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(25⁰, s, F₂₅, 2, 0) for arbitrarily large s, using
      - OOA with only one run / dual of NRT-code without redundancy [i]
  2. linear OOA(25⁰, 650, F₂₅, 2, 0) (dual of [(650, 2), 1300, 1]-NRT-code) (see above)
  3. linear OOA(25⁰, 650, F₂₅, 2, 0) (dual of [(650, 2), 1300, 1]-NRT-code) (see above)
  4. linear OOA(25⁰, 650, F₂₅, 2, 0) (dual of [(650, 2), 1300, 1]-NRT-code) (see above)
  5. linear OOA(25⁰, 650, F₂₅, 2, 0) (dual of [(650, 2), 1300, 1]-NRT-code) (see above)
  6. linear OOA(25⁰, 650, F₂₅, 2, 0) (dual of [(650, 2), 1300, 1]-NRT-code) (see above)
  7. linear OOA(25⁰, 650, F₂₅, 2, 0) (dual of [(650, 2), 1300, 1]-NRT-code) (see above)
  8. linear OOA(25⁰, 650, F₂₅, 2, 0) (dual of [(650, 2), 1300, 1]-NRT-code) (see above)
  9. linear OOA(25⁰, 650, F₂₅, 2, 0) (dual of [(650, 2), 1300, 1]-NRT-code) (see above)
  10. linear OOA(25⁰, 650, F₂₅, 2, 0) (dual of [(650, 2), 1300, 1]-NRT-code) (see above)
  11. linear OOA(25⁰, 650, F₂₅, 2, 0) (dual of [(650, 2), 1300, 1]-NRT-code) (see above)
  12. linear OOA(25⁰, 650, F₂₅, 2, 0) (dual of [(650, 2), 1300, 1]-NRT-code) (see above)
  13. linear OOA(25⁰, 650, F₂₅, 2, 0) (dual of [(650, 2), 1300, 1]-NRT-code) (see above)
  14. linear OOA(25⁰, 650, F₂₅, 2, 0) (dual of [(650, 2), 1300, 1]-NRT-code) (see above)
  15. linear OOA(25⁰, 650, F₂₅, 2, 0) (dual of [(650, 2), 1300, 1]-NRT-code) (see above)
  16. linear OOA(25⁰, 650, F₂₅, 2, 0) (dual of [(650, 2), 1300, 1]-NRT-code) (see above)
  17. linear OOA(25⁰, 650, F₂₅, 2, 0) (dual of [(650, 2), 1300, 1]-NRT-code) (see above)
  18. linear OOA(25⁰, 650, F₂₅, 2, 0) (dual of [(650, 2), 1300, 1]-NRT-code) (see above)
  19. linear OOA(25⁰, 650, F₂₅, 2, 0) (dual of [(650, 2), 1300, 1]-NRT-code) (see above)
  20. linear OOA(25⁰, 650, F₂₅, 2, 0) (dual of [(650, 2), 1300, 1]-NRT-code) (see above)
  21. linear OOA(25¹, 650, F₂₅, 2, 1) (dual of [(650, 2), 1299, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(25¹, s, F₂₅, 2, 1) for arbitrarily large s, using
      - appending 1 arbitrary column [i] based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  22. linear OOA(25¹, 650, F₂₅, 2, 1) (dual of [(650, 2), 1299, 2]-NRT-code) (see above)
  23. linear OOA(25¹, 650, F₂₅, 2, 1) (dual of [(650, 2), 1299, 2]-NRT-code) (see above)
  24. linear OOA(25³, 650, F₂₅, 2, 2) (dual of [(650, 2), 1297, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(25³, 651, F₂₅, 2, 2) (dual of [(651, 2), 1299, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(25³, 651, F₂₅, 2) (dual of [651, 648, 3]-code), using
        Hamming code H(3,25) [i]
  25. linear OOA(25¹⁰, 650, F₂₅, 2, 5) (dual of [(650, 2), 1290, 6]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(25⁰, s, F₂₅, 2, 0) for arbitrarily large s (see above)
      2. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
      3. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
      4. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
      5. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
      6. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
      7. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
      8. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
      9. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
      10. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
      11. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
      12. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
      13. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
      14. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
      15. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
      16. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
      17. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
      18. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
      19. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
      20. linear OOA(25⁰, 26, F₂₅, 2, 0) (dual of [(26, 2), 52, 1]-NRT-code) (see above)
      21. linear OOA(25¹, 26, F₂₅, 2, 1) (dual of [(26, 2), 51, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(25¹, s, F₂₅, 2, 1) for arbitrarily large s (see above)
      22. linear OOA(25¹, 26, F₂₅, 2, 1) (dual of [(26, 2), 51, 2]-NRT-code) (see above)
      23. linear OOA(25¹, 26, F₂₅, 2, 1) (dual of [(26, 2), 51, 2]-NRT-code) (see above)
      24. linear OOA(25², 26, F₂₅, 2, 2) (dual of [(26, 2), 50, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;50,25) [i]
      25. linear OOA(25⁵, 26, F₂₅, 2, 5) (dual of [(26, 2), 47, 6]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;47,25) [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 (52, 62, 1693969)-net over F₂₅	[i]		(u,Â u+v)-Construction for Nets
2	Digital (56, 67, 1693969)-net over F₂₅	[i]		(u,Â u+v)-Construction for Nets