MinT - Information on Result #1193012

Information on Result #1193012

Digital (19, 24, 58418)-net over F₉, using net defined by OOA based on linear OOA(9²⁴, 58418, F₉, 6, 5) (dual of [(58418, 6), 350484, 6]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(9²⁴, 58419, F₉, 2, 5) (dual of [(58419, 2), 116814, 6]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(9⁰, 6491, F₉, 2, 0) (dual of [(6491, 2), 12982, 1]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(9⁰, s, F₉, 2, 0) for arbitrarily large s, using
      - OOA with only one run / dual of NRT-code without redundancy [i]
  2. linear OOA(9⁰, 6491, F₉, 2, 0) (dual of [(6491, 2), 12982, 1]-NRT-code) (see above)
  3. linear OOA(9⁰, 6491, F₉, 2, 0) (dual of [(6491, 2), 12982, 1]-NRT-code) (see above)
  4. linear OOA(9⁰, 6491, F₉, 2, 0) (dual of [(6491, 2), 12982, 1]-NRT-code) (see above)
  5. linear OOA(9¹, 6491, F₉, 2, 1) (dual of [(6491, 2), 12981, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(9¹, s, F₉, 2, 1) for arbitrarily large s, using
      - appending 1 arbitrary column [i] based on linear OA(9¹, s, F₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  6. linear OOA(9¹, 6491, F₉, 2, 1) (dual of [(6491, 2), 12981, 2]-NRT-code) (see above)
  7. linear OOA(9¹, 6491, F₉, 2, 1) (dual of [(6491, 2), 12981, 2]-NRT-code) (see above)
  8. linear OOA(9⁵, 6491, F₉, 2, 2) (dual of [(6491, 2), 12977, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(9⁵, 7381, F₉, 2, 2) (dual of [(7381, 2), 14757, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(9⁵, 7381, F₉, 2) (dual of [7381, 7376, 3]-code), using
        Hamming code H(5,9) [i]
  9. linear OOA(9¹⁶, 6491, F₉, 2, 5) (dual of [(6491, 2), 12966, 6]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(9², 10, F₉, 2, 2) (dual of [(10, 2), 18, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;18,9) [i]
      2. linear OOA(9¹⁴, 6481, F₉, 2, 5) (dual of [(6481, 2), 12948, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(9¹⁴, 12962, F₉, 5) (dual of [12962, 12948, 6]-code), using
        trace code [i] based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
        a code by Danev and Olsson [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 (88, 98, 3413858)-net over F₉	[i]		(u,Â u+v)-Construction for Nets
2	Digital (95, 106, 3413858)-net over F₉	[i]		(u,Â u+v)-Construction for Nets