MinT - Information on Result #1824853

Information on Result #1824853

(45, 72, 5043)-net in base 128, using base change based on digital (36, 63, 5043)-net over F₂₅₆, using

256³ times duplication [i] based on digital (33, 60, 5043)-net over F₂₅₆, using
- net defined by OOA [i] based on linear OOA(256⁶⁰, 5043, F₂₅₆, 27, 27) (dual of [(5043, 27), 136101, 28]-NRT-code), using
  - OOA 13-folding and stacking with additional row [i] based on linear OA(256⁶⁰, 65560, F₂₅₆, 27) (dual of [65560, 65500, 28]-code), using
    - constructionÂ X applied to C([0,13]) âŠ‚ C([0,9]) [i] based on
      1. linear OA(256⁵³, 65537, F₂₅₆, 27) (dual of [65537, 65484, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
      2. linear OA(256³⁷, 65537, F₂₅₆, 19) (dual of [65537, 65500, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      3. linear OA(256⁷, 23, F₂₅₆, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,256)), using
        discarding factors / shortening the dual code based on linear OA(256⁷, 256, F₂₅₆, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
        Reedâ€“Solomon code RS(249,256) [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	(46, 73, 5043)-net in base 128	[i]		Net Duplication
2	(45, 71, 5043)-net in base 128	[i]		m-Reduction