MinT - Information on Result #1201422

Information on Result #1201422

Digital (67, 82, 2097150)-net over F₆₄, using net defined by OOA based on linear OOA(64⁸², 2097150, F₆₄, 18, 15) (dual of [(2097150, 18), 37748618, 16]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(64⁸², 8388601, F₆₄, 2, 15) (dual of [(8388601, 2), 16777120, 16]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(64⁸², 8388602, F₆₄, 2, 15) (dual of [(8388602, 2), 16777122, 16]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(64²⁵, 4194301, F₆₄, 2, 7) (dual of [(4194301, 2), 8388577, 8]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(64²⁵, 8388602, F₆₄, 7) (dual of [8388602, 8388577, 8]-code), using
        discarding factors / shortening the dual code based on linear OA(64²⁵, large, F₆₄, 7) (dual of [large, large−25, 8]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
    2. linear OOA(64⁵⁷, 4194301, F₆₄, 2, 15) (dual of [(4194301, 2), 8388545, 16]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(64⁵⁷, 8388602, F₆₄, 15) (dual of [8388602, 8388545, 16]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁵⁷, large, F₆₄, 15) (dual of [large, large−57, 16]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [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 (231, 246, 6291450)-net over F₄	[i]		Trace Code for Nets
2	Digital (149, 164, 4194300)-net over F₈	[i]		Trace Code for Nets