MinT - Information on Result #1193006

Information on Result #1193006

Digital (15, 20, 19442)-net over F₉, using net defined by OOA based on linear OOA(9²⁰, 19442, F₉, 6, 5) (dual of [(19442, 6), 116632, 6]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(9²⁰, 19443, F₉, 2, 5) (dual of [(19443, 2), 38866, 6]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(9¹, 6481, F₉, 2, 1) (dual of [(6481, 2), 12961, 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]
  2. linear OOA(9⁵, 6481, F₉, 2, 2) (dual of [(6481, 2), 12957, 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]
  3. 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 (84, 94, 3374882)-net over F₉	[i]		(u,Â u+v)-Construction for Nets
2	Digital (91, 102, 3374882)-net over F₉	[i]		(u,Â u+v)-Construction for Nets