MinT - Information on Result #1824344

Information on Result #1824344

(62, 77, 299594)-net in base 16, using base change based on digital (29, 44, 299594)-net over F₁₂₈, using

net defined by OOA [i] based on linear OOA(128⁴⁴, 299594, F₁₂₈, 15, 15) (dual of [(299594, 15), 4493866, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(128⁴⁴, 2097159, F₁₂₈, 15) (dual of [2097159, 2097115, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(128⁴⁴, 2097160, F₁₂₈, 15) (dual of [2097160, 2097116, 16]-code), using
    - constructionÂ X applied to C([0,7]) âŠ‚ C([0,6]) [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(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(128¹, 7, F₁₂₈, 1) (dual of [7, 6, 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	(63, 78, 299594)-net in base 16	[i]		Net Duplication
2	(64, 79, 299594)-net in base 16	[i]
3	(65, 80, 299594)-net in base 16	[i]