MinT - Information on Result #1198544

Information on Result #1198544

Digital (80, 107, 40881)-net over F₂₇, using net defined by OOA based on linear OOA(27¹⁰⁷, 40881, F₂₇, 27, 27) (dual of [(40881, 27), 1103680, 28]-NRT-code), using

OOA 13-folding and stacking with additional row [i] based on linear OA(27¹⁰⁷, 531454, F₂₇, 27) (dual of [531454, 531347, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(27¹⁰⁷, 531455, F₂₇, 27) (dual of [531455, 531348, 28]-code), using
  - 1 times truncation [i] based on linear OA(27¹⁰⁸, 531456, F₂₇, 28) (dual of [531456, 531348, 29]-code), using
    - constructionÂ X applied to C_e(27) âŠ‚ C_e(23) [i] based on
      1. linear OA(27¹⁰⁵, 531441, F₂₇, 28) (dual of [531441, 531336, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      2. linear OA(27⁹³, 531441, F₂₇, 24) (dual of [531441, 531348, 25]-code), using an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]
      3. linear OA(27³, 15, F₂₇, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,27) or 15-cap in PG(2,27)), using
        discarding factors / shortening the dual code based on linear OA(27³, 27, F₂₇, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
        Reedâ€“Solomon code RS(24,27) [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 (81, 108, 40881)-net over F₂₇	[i]		Net Duplication
2	Digital (82, 109, 40881)-net over F₂₇	[i]		Net Duplication