MinT - Information on Result #1195902

Information on Result #1195902

Digital (9, 16, 324)-net over F₂₅, using net defined by OOA based on linear OOA(25¹⁶, 324, F₂₅, 10, 7) (dual of [(324, 10), 3224, 8]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(25¹⁶, 649, F₂₅, 2, 7) (dual of [(649, 2), 1282, 8]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25¹⁶, 650, F₂₅, 2, 7) (dual of [(650, 2), 1284, 8]-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, using
        OOA with only one run / dual of NRT-code without redundancy [i]
    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(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, 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]
    20. linear OOA(25¹, 26, F₂₅, 2, 1) (dual of [(26, 2), 51, 2]-NRT-code) (see above)
    21. linear OOA(25¹, 26, F₂₅, 2, 1) (dual of [(26, 2), 51, 2]-NRT-code) (see above)
    22. linear OOA(25¹, 26, F₂₅, 2, 1) (dual of [(26, 2), 51, 2]-NRT-code) (see above)
    23. 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]
    24. linear OOA(25³, 26, F₂₅, 2, 3) (dual of [(26, 2), 49, 4]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;49,25) [i]
    25. linear OOA(25⁷, 26, F₂₅, 2, 7) (dual of [(26, 2), 45, 8]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;45,25) [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 (68, 82, 1198695)-net over F₂₅	[i]		(u,Â u+v)-Construction for Nets
2	Digital (72, 87, 1198695)-net over F₂₅	[i]		(u,Â u+v)-Construction for Nets