MinT - Information on Result #1824477

Information on Result #1824477

(80, 105, 174763)-net in base 32, using base change based on digital (50, 75, 174763)-net over F₁₂₈, using

128¹ times duplication [i] based on digital (49, 74, 174763)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128⁷⁴, 174763, F₁₂₈, 25, 25) (dual of [(174763, 25), 4369001, 26]-NRT-code), using
  - OOA 12-folding and stacking with additional row [i] based on linear OA(128⁷⁴, 2097157, F₁₂₈, 25) (dual of [2097157, 2097083, 26]-code), using
    - discarding factors / shortening the dual code based on linear OA(128⁷⁴, 2097160, F₁₂₈, 25) (dual of [2097160, 2097086, 26]-code), using
      - constructionÂ X applied to C([0,12]) âŠ‚ C([0,11]) [i] based on
        linear OA(128⁷³, 2097153, F₁₂₈, 25) (dual of [2097153, 2097080, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
        linear OA(128⁶⁷, 2097153, F₁₂₈, 23) (dual of [2097153, 2097086, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [i]
        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	(81, 106, 174763)-net in base 32	[i]		Net Duplication
2	(82, 107, 174763)-net in base 32	[i]		Net Duplication