MinT - Information on Result #548641

Information on Result #548641

There is no linear OA(7³⁶, 94, F₇, 30) (dual of [94, 58, 31]-code), because constructionÂ Y1 would yield

linear OA(7³⁵, 45, F₇, 30) (dual of [45, 10, 31]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(7³⁴, 37, F₇, 30) (dual of [37, 3, 31]-code), but
    - â€œHi4â€ bound on codes from Brouwerâ€™s database [i]
  2. linear OA(7¹⁰, 45, F₇, 8) (dual of [45, 35, 9]-code), but
    - discarding factors / shortening the dual code would yield linear OA(7¹⁰, 42, F₇, 8) (dual of [42, 32, 9]-code), but
      - constructionÂ Y1 [i] would yield
        linear OA(7⁹, 14, F₇, 8) (dual of [14, 5, 9]-code), but
        â€œMPaâ€ bound on codes from Brouwerâ€™s database [i]
        linear OA(7³², 42, F₇, 28) (dual of [42, 10, 29]-code), but
        discarding factors / shortening the dual code would yield linear OA(7³², 38, F₇, 28) (dual of [38, 6, 29]-code), but
        residual code [i] would yield linear OA(7⁴, 9, F₇, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,7)), but
        bound for MDS codes [i]
OA(7⁵⁸, 94, S₇, 49), but
- the linear programming bound shows that MÂ â‰¥ 10580 743749 861231 293497 451788 690805 914704 925957 518061 849209 488293 043893 822152 954067 592535 777967 / 972 197243 784671 062972 315640 073851 274697 000575 > 7⁵⁸ [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OOA(7³⁶, 94, F₇, 2, 30) (dual of [(94, 2), 152, 31]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(7³⁶, 94, F₇, 3, 30) (dual of [(94, 3), 246, 31]-NRT-code)	[i]	Depth Reduction
3	No digital (6, 36, 94)-net over F₇	[i]	Extracting Embedded Orthogonal Array