MinT - Information on Result #1201402

Information on Result #1201402

Digital (31, 46, 37451)-net over F₆₄, using net defined by OOA based on linear OOA(64⁴⁶, 37451, F₆₄, 15, 15) (dual of [(37451, 15), 561719, 16]-NRT-code), using

OOA 7-folding and stacking with additional row [i] based on linear OA(64⁴⁶, 262158, F₆₄, 15) (dual of [262158, 262112, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(64⁴⁶, 262160, F₆₄, 15) (dual of [262160, 262114, 16]-code), using
  - constructionÂ X applied to C([0,7]) âŠ‚ C([0,5]) [i] based on
    1. linear OA(64⁴³, 262145, F₆₄, 15) (dual of [262145, 262102, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
    2. linear OA(64³¹, 262145, F₆₄, 11) (dual of [262145, 262114, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (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		This result only	Method
1	Digital (32, 47, 37451)-net over F₆₄	[i]		Net Duplication
2	(54, 69, 37451)-net in base 16	[i]		Base Change