MinT - Information on Result #1071971

Information on Result #1071971

Linear OOA(3⁵, 20, F₃, 4, 3) (dual of [(20, 4), 75, 4]-NRT-code), using appending 1 arbitrary column based on linear OOA(3⁵, 20, F₃, 3, 3) (dual of [(20, 3), 55, 4]-NRT-code), using

appending kth column [i] based on linear OOA(3⁵, 20, F₃, 2, 3) (dual of [(20, 2), 35, 4]-NRT-code), using
- OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁵, 20, F₃, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,3)), using
  - doubling the cap [i] based on linear OA(3⁴, 10, F₃, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), using
    - ovoid in PG(3,Â 3) [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, 53, F₃, 4, 6) (dual of [(53, 4), 195, 7]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(3⁶⁵, 2796221, F₃, 4, 6) (dual of [(2796221, 4), 11184819, 7]-NRT-code)	[i]
3	Linear OOA(3¹⁷, 40, F₃, 4, 7) (dual of [(40, 4), 143, 8]-NRT-code)	[i]
4	Linear OOA(3¹⁸, 46, F₃, 4, 7) (dual of [(46, 4), 166, 8]-NRT-code)	[i]
5	Linear OOA(3¹⁹, 54, F₃, 4, 7) (dual of [(54, 4), 197, 8]-NRT-code)	[i]
6	Linear OOA(3¹⁵⁴, 4194320, F₃, 4, 11) (dual of [(4194320, 4), 16777126, 12]-NRT-code)	[i]	Generalized (u,Â u+v)-Construction for OOAs
7	Linear OOA(3¹²³, 4194320, F₃, 4, 9) (dual of [(4194320, 4), 16777157, 10]-NRT-code)	[i]	Generalized (u,Â u+v)-Construction for OOAs