MinT - Information on Result #1179396

Information on Result #1179396

Digital (63, 69, 2796733)-net over F₃, using net defined by OOA based on linear OOA(3⁶⁹, 2796733, F₃, 6, 6) (dual of [(2796733, 6), 16780329, 7]-NRT-code), using

appending kth column [i] based on linear OOA(3⁶⁹, 2796733, F₃, 5, 6) (dual of [(2796733, 5), 13983596, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁹, 532, F₃, 5, 3) (dual of [(532, 5), 2651, 4]-NRT-code), using
    - appending 2 arbitrary columns [i] based on linear OOA(3⁹, 532, F₃, 3, 3) (dual of [(532, 3), 1587, 4]-NRT-code), using
      - appending kth column [i] based on linear OOA(3⁹, 532, F₃, 2, 3) (dual of [(532, 2), 1055, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁹, 532, F₃, 3) (dual of [532, 523, 4]-code or 532-cap in PG(8,3)), using
        caps completed using a computer search [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 (225, 237, 6991033)-net over F₃	[i]		(u,Â u+v)-Construction for Nets