MinT - Information on Result #1191114

Information on Result #1191114

Digital (33, 40, 174768)-net over F₈, using net defined by OOA based on linear OOA(8⁴⁰, 174768, F₈, 7, 7) (dual of [(174768, 7), 1223336, 8]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OA(8⁴⁰, 524305, F₈, 7) (dual of [524305, 524265, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(8⁴⁰, 524306, F₈, 7) (dual of [524306, 524266, 8]-code), using
  - trace code [i] based on linear OA(64²⁰, 262153, F₆₄, 7) (dual of [262153, 262133, 8]-code), using
    - constructionÂ X4 applied to C([0,3]) âŠ‚ C([0,2]) [i] based on
      1. linear OA(64¹⁹, 262145, F₆₄, 7) (dual of [262145, 262126, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
      2. linear OA(64¹³, 262145, F₆₄, 5) (dual of [262145, 262132, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’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(64⁷, 8, F₆₄, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,64)), using
        dual of repetition code with length 8 [i]
      4. linear OA(64¹, 8, F₆₄, 1) (dual of [8, 7, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(64¹, 64, F₆₄, 1) (dual of [64, 63, 2]-code), using
        Reedâ€“Solomon code RS(63,64) [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 (132, 146, 2571510)-net over F₈	[i]		(u,Â u+v)-Construction for Nets
2	Digital (139, 154, 2571510)-net over F₈	[i]		(u,Â u+v)-Construction for Nets