MinT - Information on Result #994122

Information on Result #994122

Linear OOA(3¹⁷, 307328, F₃, 3, 3) (dual of [(307328, 3), 921967, 4]-NRT-code), using appending kth column based on linear OOA(3¹⁷, 307328, F₃, 2, 3) (dual of [(307328, 2), 614639, 4]-NRT-code), using

OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3¹⁷, 307328, F₃, 3) (dual of [307328, 307311, 4]-code or 307328-cap in PG(16,3)), using
- product of two projective caps and 2-cap in AG(1,Â 3) [i] based on
  1. linear OA(3⁶, 56, F₃, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
    - the Hill cap [i]
  2. linear OA(3¹¹, 2744, F₃, 3) (dual of [2744, 2733, 4]-code or 2744-cap in PG(10,3)), using
    - caps completed using a computer search [i]

Mode: Constructive and 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		Method
1	Linear OOA(3¹⁷, 307328, F₃, 4, 3) (dual of [(307328, 4), 1229295, 4]-NRT-code)	[i]	Appending Arbitrary Columns
2	Linear OOA(3¹⁷, 307328, F₃, 5, 3) (dual of [(307328, 5), 1536623, 4]-NRT-code)	[i]	Appending Arbitrary Columns
3	Digital (14, 17, 307328)-net over F₃	[i]	Net Defined by OOA