MinT - Information on Result #1203606

Information on Result #1203606

Digital (33, 48, 299596)-net over F₁₂₈, using net defined by OOA based on linear OOA(128⁴⁸, 299596, F₁₂₈, 15, 15) (dual of [(299596, 15), 4493892, 16]-NRT-code), using

OOA 7-folding and stacking with additional row [i] based on linear OA(128⁴⁸, 2097173, F₁₂₈, 15) (dual of [2097173, 2097125, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(128⁴⁸, 2097176, F₁₂₈, 15) (dual of [2097176, 2097128, 16]-code), using
  - constructionÂ X applied to C([0,7]) âŠ‚ C([0,4]) [i] based on
    1. linear OA(128⁴³, 2097153, F₁₂₈, 15) (dual of [2097153, 2097110, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
    2. linear OA(128²⁵, 2097153, F₁₂₈, 9) (dual of [2097153, 2097128, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (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 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		Method
1	Digital (34, 49, 299596)-net over F₁₂₈	[i]	Net Duplication
2	(69, 84, 299596)-net in base 16	[i]	Base Change
3	(41, 56, 299596)-net in base 64	[i]	Base Change