MinT - Information on Result #1182851

Information on Result #1182851

Linear OOA(3⁷⁹, 3541672, F₃, 9, 7) (dual of [(3541672, 9), 31874969, 8]-NRT-code), using OOA stacking with additional row based on linear OOA(3⁷⁹, 3541673, F₃, 3, 7) (dual of [(3541673, 3), 10624940, 8]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3¹⁸, 745472, F₃, 3, 3) (dual of [(745472, 3), 2236398, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(3¹⁸, 745472, F₃, 2, 3) (dual of [(745472, 2), 1490926, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3¹⁸, 745472, F₃, 3) (dual of [745472, 745454, 4]-code or 745472-cap in PG(17,3)), using
      - large caps in PG(u,Â 3) [i]
2. 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.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (72, 79, 3541672)-net over F₃	[i]		Net Defined by OOA