MinT - Information on Result #1197222

Information on Result #1197222

Digital (6, 11, 1054)-net over F₂₇, using net defined by OOA based on linear OOA(27¹¹, 1054, F₂₇, 5, 5) (dual of [(1054, 5), 5259, 6]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OA(27¹¹, 2109, F₂₇, 5) (dual of [2109, 2098, 6]-code), using
- (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
  1. linear OA(27¹, 703, F₂₇, 1) (dual of [703, 702, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(27¹, s, F₂₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
  2. linear OA(27³, 703, F₂₇, 2) (dual of [703, 700, 3]-code), using
    - discarding factors / shortening the dual code based on linear OA(27³, 728, F₂₇, 2) (dual of [728, 725, 3]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 27²âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
  3. linear OA(27⁷, 703, F₂₇, 5) (dual of [703, 696, 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 (47, 57, 1678774)-net over F₂₇	[i]		(u,Â u+v)-Construction for Nets
2	Digital (51, 62, 1678774)-net over F₂₇	[i]		(u,Â u+v)-Construction for Nets