MinT - Information on Result #1201266

Information on Result #1201266

Digital (27, 40, 43693)-net over F₆₄, using net defined by OOA based on linear OOA(64⁴⁰, 43693, F₆₄, 13, 13) (dual of [(43693, 13), 567969, 14]-NRT-code), using

OOA 6-folding and stacking with additional row [i] based on linear OA(64⁴⁰, 262159, F₆₄, 13) (dual of [262159, 262119, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(64⁴⁰, 262160, F₆₄, 13) (dual of [262160, 262120, 14]-code), using
  - constructionÂ X applied to C([0,6]) âŠ‚ C([0,4]) [i] based on
    1. linear OA(64³⁷, 262145, F₆₄, 13) (dual of [262145, 262108, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
    2. linear OA(64²⁵, 262145, F₆₄, 9) (dual of [262145, 262120, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
    3. linear OA(64³, 15, F₆₄, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,64) or 15-cap in PG(2,64)), using
      - discarding factors / shortening the dual code based on linear OA(64³, 64, F₆₄, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
        Reedâ€“Solomon code RS(61,64) [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		Method
1	Digital (28, 41, 43693)-net over F₆₄	[i]	Net Duplication
2	(35, 48, 43693)-net in base 32	[i]	Base Change
3	(47, 60, 43693)-net in base 16	[i]	Base Change