MinT - Information on Result #1010390

Information on Result #1010390

Linear OOA(3¹⁷, 53, F₃, 3, 6) (dual of [(53, 3), 142, 7]-NRT-code), using (u,Â u+v)-construction 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(3¹², 33, F₃, 3, 6) (dual of [(33, 3), 87, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (6, 12, 33)-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		Method
1	Linear OOA(3¹³⁷, 2796254, F₃, 3, 12) (dual of [(2796254, 3), 8388625, 13]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(3¹⁵⁹, 3188703, F₃, 3, 12) (dual of [(3188703, 3), 9565950, 13]-NRT-code)	[i]
3	Linear OOA(3¹⁷⁹, 5592455, F₃, 3, 12) (dual of [(5592455, 3), 16777186, 13]-NRT-code)	[i]
4	Linear OOA(3¹³⁸, 2796254, F₃, 3, 13) (dual of [(2796254, 3), 8388624, 14]-NRT-code)	[i]
5	Linear OOA(3¹⁹⁵, 5592455, F₃, 3, 13) (dual of [(5592455, 3), 16777170, 14]-NRT-code)	[i]
6	Linear OOA(3¹⁷, 52, F₃, 4, 6) (dual of [(52, 4), 191, 7]-NRT-code)	[i]	OOA Stacking with Additional Row
7	Linear OOA(3¹⁷, 52, F₃, 5, 6) (dual of [(52, 5), 243, 7]-NRT-code)	[i]	OOA Stacking with Additional Row