MinT - Information on Result #1080847

Information on Result #1080847

Linear OOA(3¹⁹, 54, F₃, 4, 7) (dual of [(54, 4), 197, 8]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁵, 20, F₃, 4, 3) (dual of [(20, 4), 75, 4]-NRT-code), using
- appending 1 arbitrary column [i] 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]
linear OOA(3¹⁴, 34, F₃, 4, 7) (dual of [(34, 4), 122, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (7, 14, 34)-net over F₃, using
  - linear code embedding found in a computer search [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁵⁵, 2097204, F₃, 4, 14) (dual of [(2097204, 4), 8388661, 15]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(3¹⁶⁹, 2097204, F₃, 4, 15) (dual of [(2097204, 4), 8388647, 16]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs