MinT - Information on Result #1184444

Information on Result #1184444

Digital (197, 214, 1195745)-net over F₃, using net defined by OOA based on linear OOA(3²¹⁴, 1195745, F₃, 18, 17) (dual of [(1195745, 18), 21523196, 18]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(3²¹⁴, 4782981, F₃, 2, 17) (dual of [(4782981, 2), 9565748, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3²¹⁴, 4782984, F₃, 2, 17) (dual of [(4782984, 2), 9565754, 18]-NRT-code), using
  - trace code [i] based on linear OOA(9¹⁰⁷, 2391492, F₉, 2, 17) (dual of [(2391492, 2), 4782877, 18]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(9¹⁰⁷, 4782984, F₉, 17) (dual of [4782984, 4782877, 18]-code), using
      - constructionÂ X applied to C_e(16) âŠ‚ C_e(14) [i] based on
        linear OA(9¹⁰⁶, 4782969, F₉, 17) (dual of [4782969, 4782863, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
        linear OA(9⁹², 4782969, F₉, 15) (dual of [4782969, 4782877, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
        linear OA(9¹, 15, F₉, 1) (dual of [15, 14, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(9¹, s, F₉, 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 (198, 215, 1195745)-net over F₃	[i]		Net Duplication
2	Digital (211, 228, 1195767)-net over F₃	[i]		(u,Â u+v)-Construction for Nets