MinT - Information on Result #1185878

Information on Result #1185878

Digital (59, 66, 2796241)-net over F₄, using net defined by OOA based on linear OOA(4⁶⁶, 2796241, F₄, 9, 7) (dual of [(2796241, 9), 25166103, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(4⁶⁶, 2796242, F₄, 3, 7) (dual of [(2796242, 3), 8388660, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(4⁵, 41, F₄, 3, 3) (dual of [(41, 3), 118, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(4⁵, 41, F₄, 2, 3) (dual of [(41, 2), 77, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(4⁵, 41, F₄, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
        a cap found by Tallinii [i]
  2. linear OOA(4⁶¹, 2796201, F₄, 3, 7) (dual of [(2796201, 3), 8388542, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(4⁶¹, large, F₄, 7) (dual of [large, large−61, 8]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [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		Method
1	Digital (211, 225, 6391354)-net over F₄	[i]	(u,Â u+v)-Construction for Nets
2	Digital (212, 226, 7589725)-net over F₄	[i]
3	Digital (222, 237, 6391354)-net over F₄	[i]
4	Digital (223, 238, 7589725)-net over F₄	[i]