MinT - Information on Result #1179392

Information on Result #1179392

Digital (61, 67, 2796313)-net over F₃, using net defined by OOA based on linear OOA(3⁶⁷, 2796313, F₃, 6, 6) (dual of [(2796313, 6), 16777811, 7]-NRT-code), using

appending kth column [i] based on linear OOA(3⁶⁷, 2796313, F₃, 5, 6) (dual of [(2796313, 5), 13981498, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁷, 112, F₃, 5, 3) (dual of [(112, 5), 553, 4]-NRT-code), using
    - appending 2 arbitrary columns [i] based on linear OOA(3⁷, 112, F₃, 3, 3) (dual of [(112, 3), 329, 4]-NRT-code), using
      - appending kth column [i] based on linear OOA(3⁷, 112, F₃, 2, 3) (dual of [(112, 2), 217, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁷, 112, F₃, 3) (dual of [112, 105, 4]-code or 112-cap in PG(6,3)), using
        doubling the cap [i] based on linear OA(3⁶, 56, F₃, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
        the Hill cap [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 (223, 235, 6990613)-net over F₃	[i]		(u,Â u+v)-Construction for Nets
2	Digital (237, 250, 6990613)-net over F₃	[i]		(u,Â u+v)-Construction for Nets