MinT - Information on Result #1071973

Information on Result #1071973

Linear OOA(3⁷, 112, F₃, 4, 3) (dual of [(112, 4), 441, 4]-NRT-code), using appending 1 arbitrary column based on linear OOA(3⁷, 112, F₃, 3, 3) (dual of [(112, 3), 329, 4]-NRT-code), using

appending kth column [i] based on linear OOA(3⁷, 112, F₃, 2, 3) (dual of [(112, 2), 217, 4]-NRT-code), using
- OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁷, 112, F₃, 3) (dual of [112, 105, 4]-code or 112-cap in PG(6,3)), using
  - doubling the cap [i] based on linear OA(3⁶, 56, F₃, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
    - the Hill cap [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(3⁶⁷, 2796313, F₃, 4, 6) (dual of [(2796313, 4), 11185185, 7]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(3¹⁵⁶, 4194412, F₃, 4, 11) (dual of [(4194412, 4), 16777492, 12]-NRT-code)	[i]	Generalized (u,Â u+v)-Construction for OOAs
3	Linear OOA(3¹⁴¹, 4194412, F₃, 4, 10) (dual of [(4194412, 4), 16777507, 11]-NRT-code)	[i]
4	Linear OOA(3¹²⁵, 4194412, F₃, 4, 9) (dual of [(4194412, 4), 16777523, 10]-NRT-code)	[i]