MinT - Information on Result #1841329

Information on Result #1841329

(17, 24, 699053)-net in base 64, using net defined by OOA based on OOA(64²⁴, 699053, S₆₄, 7, 7), using

OOA 3-folding and stacking with additional row [i] based on OA(64²⁴, 2097160, S₆₄, 7), using
- discarding factors based on OA(64²⁴, 2097161, S₆₄, 7), using
  - discarding parts of the base [i] based on linear OA(128²⁰, 2097161, F₁₂₈, 7) (dual of [2097161, 2097141, 8]-code), using
    - constructionÂ X4 applied to C([0,3]) âŠ‚ C([0,2]) [i] based on
      1. linear OA(128¹⁹, 2097153, F₁₂₈, 7) (dual of [2097153, 2097134, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
      2. linear OA(128¹³, 2097153, F₁₂₈, 5) (dual of [2097153, 2097140, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
      3. linear OA(128⁷, 8, F₁₂₈, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,128)), using
        dual of repetition code with length 8 [i]
      4. linear OA(128¹, 8, F₁₂₈, 1) (dual of [8, 7, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(128¹, 128, F₁₂₈, 1) (dual of [128, 127, 2]-code), using
        Reedâ€“Solomon code RS(127,128) [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	(63, 77, 1897424)-net in base 64	[i]		(u,Â u+v)-Construction for Nets
2	(66, 81, 1897424)-net in base 64	[i]		(u,Â u+v)-Construction for Nets