MinT - Information on Result #1195826

Information on Result #1195826

Digital (6, 11, 901)-net over F₂₅, using net defined by OOA based on linear OOA(25¹¹, 901, F₂₅, 5, 5) (dual of [(901, 5), 4494, 6]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OA(25¹¹, 1803, F₂₅, 5) (dual of [1803, 1792, 6]-code), using
- (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
  1. linear OA(25¹, 601, F₂₅, 1) (dual of [601, 600, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
  2. linear OA(25³, 601, F₂₅, 2) (dual of [601, 598, 3]-code), using
    - discarding factors / shortening the dual code based on linear OA(25³, 624, F₂₅, 2) (dual of [624, 621, 3]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 624Â = 25²âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
  3. linear OA(25⁷, 601, F₂₅, 5) (dual of [601, 594, 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, 1678621)-net over F₂₅	[i]		(u,Â u+v)-Construction for Nets
2	Digital (51, 62, 1678621)-net over F₂₅	[i]		(u,Â u+v)-Construction for Nets