MinT - Information on Result #1179398

Information on Result #1179398

Digital (64, 70, 2797417)-net over F₃, using net defined by OOA based on linear OOA(3⁷⁰, 2797417, F₃, 6, 6) (dual of [(2797417, 6), 16784432, 7]-NRT-code), using

appending kth column [i] based on linear OOA(3⁷⁰, 2797417, F₃, 5, 6) (dual of [(2797417, 5), 13987015, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹⁰, 1216, F₃, 5, 3) (dual of [(1216, 5), 6070, 4]-NRT-code), using
    - appending 2 arbitrary columns [i] based on linear OOA(3¹⁰, 1216, F₃, 3, 3) (dual of [(1216, 3), 3638, 4]-NRT-code), using
      - appending kth column [i] based on linear OOA(3¹⁰, 1216, F₃, 2, 3) (dual of [(1216, 2), 2422, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3¹⁰, 1216, F₃, 3) (dual of [1216, 1206, 4]-code or 1216-cap in PG(9,3)), using
        large caps in PG(u,Â 3) [i]
  2. linear OOA(3⁶⁰, 2796201, F₃, 5, 6) (dual of [(2796201, 5), 13980945, 7]-NRT-code), using
    - OA 3-folding and stacking [i] based on linear OA(3⁶⁰, large, F₃, 6) (dual of [large, large−60, 7]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (226, 238, 6991717)-net over F₃	[i]		(u,Â u+v)-Construction for Nets