MinT - Information on Result #1010417

Information on Result #1010417

Linear OOA(3⁶⁶, 2796221, F₃, 3, 7) (dual of [(2796221, 3), 8388597, 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(3⁶¹, 2796201, F₃, 3, 7) (dual of [(2796201, 3), 8388542, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3⁶¹, large, F₃, 7) (dual of [large, large−61, 8]-code), using
  - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3⁸⁶, 5592442, F₃, 3, 7) (dual of [(5592442, 3), 16777240, 8]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(3²²⁶, 5592424, F₃, 3, 15) (dual of [(5592424, 3), 16777046, 16]-NRT-code)	[i]
3	Linear OOA(3²²⁷, 5592432, F₃, 3, 15) (dual of [(5592432, 3), 16777069, 16]-NRT-code)	[i]
4	Linear OOA(3⁶⁶, 2796220, F₃, 4, 7) (dual of [(2796220, 4), 11184814, 8]-NRT-code)	[i]	OOA Stacking with Additional Row
5	Linear OOA(3⁶⁶, 2796220, F₃, 5, 7) (dual of [(2796220, 5), 13981034, 8]-NRT-code)	[i]
6	Linear OOA(3⁶⁶, 2796220, F₃, 9, 7) (dual of [(2796220, 9), 25165914, 8]-NRT-code)	[i]