MinT - Information on Result #1190976

Information on Result #1190976

Digital (15, 20, 12098)-net over F₈, using net defined by OOA based on linear OOA(8²⁰, 12098, F₈, 6, 5) (dual of [(12098, 6), 72568, 6]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(8²⁰, 12099, F₈, 2, 5) (dual of [(12099, 2), 24178, 6]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(8¹, 4033, F₈, 2, 1) (dual of [(4033, 2), 8065, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8¹, s, F₈, 2, 1) for arbitrarily large s, using
      - appending 1 arbitrary column [i] based on linear OA(8¹, s, F₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. linear OOA(8⁵, 4033, F₈, 2, 2) (dual of [(4033, 2), 8061, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8⁵, 4681, F₈, 2, 2) (dual of [(4681, 2), 9357, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(8⁵, 4681, F₈, 2) (dual of [4681, 4676, 3]-code), using
        Hamming code H(5,8) [i]
  3. linear OOA(8¹⁴, 4033, F₈, 2, 5) (dual of [(4033, 2), 8052, 6]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(8¹⁴, 8066, F₈, 5) (dual of [8066, 8052, 6]-code), using
      - trace code [i] based on linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 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, 3367538)-net over F₈	[i]		(u,Â u+v)-Construction for Nets
2	Digital (91, 102, 3367538)-net over F₈	[i]		(u,Â u+v)-Construction for Nets