MinT - Information on Result #3211011

Information on Result #3211011

Digital (151, 171, 419434)-net over F₄, using t-expansion based on digital (150, 171, 419434)-net over F₄, using

net defined by OOA [i] based on linear OOA(4¹⁷¹, 419434, F₄, 21, 21) (dual of [(419434, 21), 8807943, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(4¹⁷¹, 4194341, F₄, 21) (dual of [4194341, 4194170, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁷¹, 4194342, F₄, 21) (dual of [4194342, 4194171, 22]-code), using
    - constructionÂ X applied to C_e(20) âŠ‚ C_e(16) [i] based on
      1. linear OA(4¹⁶⁶, 4194304, F₄, 21) (dual of [4194304, 4194138, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      2. linear OA(4¹³³, 4194304, F₄, 17) (dual of [4194304, 4194171, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      3. linear OA(4⁵, 38, F₄, 3) (dual of [38, 33, 4]-code or 38-cap in PG(4,4)), using
        discarding factors / shortening the dual code based on linear OA(4⁵, 41, F₄, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
        a cap found by Tallinii [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 (152, 172, 419434)-net over F₄	[i]		Net Duplication
2	Digital (153, 173, 419434)-net over F₄	[i]		Net Duplication