MinT - Information on Result #1198814

Information on Result #1198814

Digital (12, 19, 10923)-net over F₃₂, using net defined by OOA based on linear OOA(32¹⁹, 10923, F₃₂, 7, 7) (dual of [(10923, 7), 76442, 8]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OA(32¹⁹, 32770, F₃₂, 7) (dual of [32770, 32751, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(32¹⁹, 32771, F₃₂, 7) (dual of [32771, 32752, 8]-code), using
  - constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
    1. linear OA(32¹⁹, 32768, F₃₂, 7) (dual of [32768, 32749, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    2. linear OA(32¹⁶, 32768, F₃₂, 6) (dual of [32768, 32752, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
    3. linear OA(32⁰, 3, F₃₂, 0) (dual of [3, 3, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 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		Method
1	Digital (15, 22, 10956)-net over F₃₂	[i]	(u,Â u+v)-Construction for Nets
2	Digital (16, 23, 11948)-net over F₃₂	[i]
3	Digital (17, 24, 14059)-net over F₃₂	[i]
4	Digital (71, 85, 1209294)-net over F₃₂	[i]
5	Digital (75, 90, 1209294)-net over F₃₂	[i]
6	(69, 83, 1209294)-net in base 32	[i]
7	(73, 88, 1209294)-net in base 32	[i]