MinT - Information on Result #1841547

Information on Result #1841547

(29, 50, 1639)-net in base 64, using net defined by OOA based on OOA(64⁵⁰, 1639, S₆₄, 21, 21), using

OOA 10-folding and stacking with additional row [i] based on OA(64⁵⁰, 16391, S₆₄, 21), using
- 1 times code embedding in larger space [i] based on OA(64⁴⁹, 16390, S₆₄, 21), using
  - discarding parts of the base [i] based on linear OA(128⁴², 16390, F₁₂₈, 21) (dual of [16390, 16348, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,9]) [i] based on
      1. linear OA(128⁴¹, 16385, F₁₂₈, 21) (dual of [16385, 16344, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      2. linear OA(128³⁷, 16385, F₁₂₈, 19) (dual of [16385, 16348, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      3. linear OA(128¹, 5, F₁₂₈, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(128¹, s, F₁₂₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: Constructive.

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	(30, 50, 1639)-net in base 64	[i]		t-Expansion
2	(30, 51, 1639)-net in base 64	[i]		Net Duplication
3	(31, 52, 1639)-net in base 64	[i]
4	(32, 53, 1639)-net in base 64	[i]
5	(54, 75, 1638)-net in base 16	[i]		Base Change
6	(39, 60, 1638)-net in base 32	[i]		Base Change