MinT - Information on Result #1191102

Information on Result #1191102

Digital (26, 33, 10927)-net over F₈, using net defined by OOA based on linear OOA(8³³, 10927, F₈, 7, 7) (dual of [(10927, 7), 76456, 8]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OA(8³³, 32782, F₈, 7) (dual of [32782, 32749, 8]-code), using
- 1 times code embedding in larger space [i] based on linear OA(8³², 32781, F₈, 7) (dual of [32781, 32749, 8]-code), using
  - constructionÂ X4 applied to C([0,3]) âŠ‚ C([0,2]) [i] based on
    1. linear OA(8³¹, 32769, F₈, 7) (dual of [32769, 32738, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 8¹⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
    2. linear OA(8²¹, 32769, F₈, 5) (dual of [32769, 32748, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 8¹⁰âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
    3. linear OA(8¹¹, 12, F₈, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,8)), using
      - dual of repetition code with length 12 [i]
    4. linear OA(8¹, 12, F₈, 1) (dual of [12, 11, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(8¹, 511, F₈, 1) (dual of [511, 510, 2]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 511Â = 8³âˆ’1, defining interval IÂ =Â [0,0], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 2 [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 (125, 139, 2407669)-net over F₈	[i]		(u,Â u+v)-Construction for Nets
2	Digital (132, 147, 2407669)-net over F₈	[i]		(u,Â u+v)-Construction for Nets