MinT - Information on Result #3266817

Information on Result #3266817

Digital (23, 40, 514)-net over F₆₄, using 64² times duplication based on digital (21, 38, 514)-net over F₆₄, using

net defined by OOA [i] based on linear OOA(64³⁸, 514, F₆₄, 17, 17) (dual of [(514, 17), 8700, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(64³⁸, 4113, F₆₄, 17) (dual of [4113, 4075, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(64³⁸, 4114, F₆₄, 17) (dual of [4114, 4076, 18]-code), using
    - constructionÂ X applied to C([0,8]) âŠ‚ C([0,5]) [i] based on
      1. linear OA(64³³, 4097, F₆₄, 17) (dual of [4097, 4064, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 64⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
      2. linear OA(64²¹, 4097, F₆₄, 11) (dual of [4097, 4076, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 64⁴âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]
      3. linear OA(64⁵, 17, F₆₄, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,64)), using
        discarding factors / shortening the dual code based on linear OA(64⁵, 64, F₆₄, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
        Reedâ€“Solomon code RS(59,64) [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	(31, 48, 514)-net in base 32	[i]		Base Change