MinT - Information on Result #1080848

Information on Result #1080848

Linear OOA(3²⁰, 68, F₃, 4, 7) (dual of [(68, 4), 252, 8]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁶, 56, F₃, 4, 3) (dual of [(56, 4), 218, 4]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(3⁶, 56, F₃, 3, 3) (dual of [(56, 3), 162, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(3⁶, 56, F₃, 2, 3) (dual of [(56, 2), 106, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [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]
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(3¹⁵⁶, 2097218, F₃, 4, 14) (dual of [(2097218, 4), 8388716, 15]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(3¹⁷⁰, 2097218, F₃, 4, 15) (dual of [(2097218, 4), 8388702, 16]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs