MinT - Information on Result #1010406

Information on Result #1010406

Linear OOA(3¹⁷, 40, F₃, 3, 7) (dual of [(40, 3), 103, 8]-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, 20, F₃, 3, 7) (dual of [(20, 3), 48, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (5, 12, 20)-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(3¹⁵³, 2796241, F₃, 3, 14) (dual of [(2796241, 3), 8388570, 15]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(3¹⁸⁷, 3188690, F₃, 3, 14) (dual of [(3188690, 3), 9565883, 15]-NRT-code)	[i]
3	Linear OOA(3²¹¹, 5592442, F₃, 3, 14) (dual of [(5592442, 3), 16777115, 15]-NRT-code)	[i]
4	Linear OOA(3¹⁶⁷, 2796241, F₃, 3, 15) (dual of [(2796241, 3), 8388556, 16]-NRT-code)	[i]
5	Linear OOA(3²⁰¹, 3188690, F₃, 3, 15) (dual of [(3188690, 3), 9565869, 16]-NRT-code)	[i]
6	Linear OOA(3²²⁷, 5592442, F₃, 3, 15) (dual of [(5592442, 3), 16777099, 16]-NRT-code)	[i]
7	Linear OOA(3¹⁷, 39, F₃, 4, 7) (dual of [(39, 4), 139, 8]-NRT-code)	[i]	OOA Stacking with Additional Row
8	Linear OOA(3¹⁷, 39, F₃, 5, 7) (dual of [(39, 5), 178, 8]-NRT-code)	[i]
9	Linear OOA(3¹⁷, 39, F₃, 9, 7) (dual of [(39, 9), 334, 8]-NRT-code)	[i]