MinT - Information on Result #1179348

Information on Result #1179348

Digital (33, 39, 6568)-net over F₃, using net defined by OOA based on linear OOA(3³⁹, 6568, F₃, 6, 6) (dual of [(6568, 6), 39369, 7]-NRT-code), using

appending kth column [i] based on linear OOA(3³⁹, 6568, F₃, 5, 6) (dual of [(6568, 5), 32801, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(3³⁹, 19704, F₃, 6) (dual of [19704, 19665, 7]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3³⁸, 19703, F₃, 6) (dual of [19703, 19665, 7]-code), using
    - constructionÂ X4 applied to C_e(6) âŠ‚ C_e(3) [i] based on
      1. linear OA(3³⁷, 19683, F₃, 7) (dual of [19683, 19646, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      2. linear OA(3¹⁹, 19683, F₃, 4) (dual of [19683, 19664, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      3. linear OA(3¹⁹, 20, F₃, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,3)), using
        dual of repetition code with length 20 [i]
      4. linear OA(3¹, 20, F₃, 1) (dual of [20, 19, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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 (207, 219, 5598968)-net over F₃	[i]		(u,Â u+v)-Construction for Nets
2	Digital (222, 235, 5598968)-net over F₃	[i]		(u,Â u+v)-Construction for Nets