MinT - Information on Result #1178954

Information on Result #1178954

Digital (19, 24, 1100)-net over F₃, using net defined by OOA based on linear OOA(3²⁴, 1100, F₃, 5, 5) (dual of [(1100, 5), 5476, 6]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(3²⁴, 1101, F₃, 2, 5) (dual of [(1101, 2), 2178, 6]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3², 4, F₃, 2, 2) (dual of [(4, 2), 6, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;6,3) [i]
  2. linear OOA(3²², 1097, F₃, 2, 5) (dual of [(1097, 2), 2172, 6]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3²², 2194, F₃, 5) (dual of [2194, 2172, 6]-code), using
      - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
        linear OA(3²², 2187, F₃, 5) (dual of [2187, 2165, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(3¹⁵, 2187, F₃, 4) (dual of [2187, 2172, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(3⁰, 7, F₃, 0) (dual of [7, 7, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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 (162, 172, 6711980)-net over F₃	[i]		(u,Â u+v)-Construction for Nets
2	Digital (177, 188, 6711980)-net over F₃	[i]		(u,Â u+v)-Construction for Nets