MinT - Information on Result #1197622

Information on Result #1197622

Digital (33, 45, 88574)-net over F₂₇, using net defined by OOA based on linear OOA(27⁴⁵, 88574, F₂₇, 12, 12) (dual of [(88574, 12), 1062843, 13]-NRT-code), using

OA 6-folding and stacking [i] based on linear OA(27⁴⁵, 531444, F₂₇, 12) (dual of [531444, 531399, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(27⁴⁵, 531445, F₂₇, 12) (dual of [531445, 531400, 13]-code), using
  - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
    1. linear OA(27⁴⁵, 531441, F₂₇, 12) (dual of [531441, 531396, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
    2. linear OA(27⁴¹, 531441, F₂₇, 11) (dual of [531441, 531400, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
    3. linear OA(27⁰, 4, F₂₇, 0) (dual of [4, 4, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(27⁰, s, F₂₇, 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 (39, 51, 88602)-net over F₂₇	[i]	(u,Â u+v)-Construction for Nets
2	Digital (40, 52, 88612)-net over F₂₇	[i]
3	Digital (41, 53, 88622)-net over F₂₇	[i]
4	Digital (42, 54, 88630)-net over F₂₇	[i]
5	Digital (43, 55, 88640)-net over F₂₇	[i]
6	(41, 53, 88656)-net in base 27	[i]
7	(43, 55, 88674)-net in base 27	[i]