MinT - Information on Result #555890

Information on Result #555890

There is no linear OOA(3⁹⁹, 99, F₃, 2, 69) (dual of [(99, 2), 99, 70]-NRT-code), because 6 step m-reduction would yield linear OA(3⁹³, 99, F₃, 63) (dual of [99, 6, 64]-code), but

residual code [i] would yield linear OA(3³⁰, 35, F₃, 21) (dual of [35, 5, 22]-code), but
- residual code [i] would yield linear OA(3⁹, 13, F₃, 7) (dual of [13, 4, 8]-code), but
  - 1 times truncation [i] would yield linear OA(3⁸, 12, F₃, 6) (dual of [12, 4, 7]-code), but
    - residual code [i] would yield linear OA(3², 5, F₃, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,3)), but
      - improvement by Maruta on the Griesmer bound [i]

Mode: Bound (linear).

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	No linear OOA(3⁹⁹, 99, F₃, 3, 69) (dual of [(99, 3), 198, 70]-NRT-code)	[i]		Depth Reduction
2	No linear OOA(3⁹⁹, 99, F₃, 4, 69) (dual of [(99, 4), 297, 70]-NRT-code)	[i]
3	No linear OOA(3⁹⁹, 99, F₃, 5, 69) (dual of [(99, 5), 396, 70]-NRT-code)	[i]