MinT - Information on Result #1824569

Information on Result #1824569

(51, 70, 233019)-net in base 64, using base change based on digital (41, 60, 233019)-net over F₁₂₈, using

net defined by OOA [i] based on linear OOA(128⁶⁰, 233019, F₁₂₈, 19, 19) (dual of [(233019, 19), 4427301, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(128⁶⁰, 2097172, F₁₂₈, 19) (dual of [2097172, 2097112, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(128⁶⁰, 2097176, F₁₂₈, 19) (dual of [2097176, 2097116, 20]-code), using
    - constructionÂ X applied to C([0,9]) âŠ‚ C([0,6]) [i] based on
      1. linear OA(128⁵⁵, 2097153, F₁₂₈, 19) (dual of [2097153, 2097098, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      2. linear OA(128³⁷, 2097153, F₁₂₈, 13) (dual of [2097153, 2097116, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
      3. linear OA(128⁵, 23, F₁₂₈, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,128)), using
        discarding factors / shortening the dual code based on linear OA(128⁵, 128, F₁₂₈, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
        Reedâ€“Solomon code RS(123,128) [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	(52, 71, 233019)-net in base 64	[i]		Net Duplication
2	(53, 72, 233019)-net in base 64	[i]		Net Duplication