MinT - Information on Result #1195682

Information on Result #1195682

Digital (82, 108, 10084)-net over F₁₆, using net defined by OOA based on linear OOA(16¹⁰⁸, 10084, F₁₆, 26, 26) (dual of [(10084, 26), 262076, 27]-NRT-code), using

OA 13-folding and stacking [i] based on linear OA(16¹⁰⁸, 131092, F₁₆, 26) (dual of [131092, 130984, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(16¹⁰⁸, 131094, F₁₆, 26) (dual of [131094, 130986, 27]-code), using
  - trace code [i] based on linear OA(256⁵⁴, 65547, F₂₅₆, 26) (dual of [65547, 65493, 27]-code), using
    - constructionÂ X applied to C_e(25) âŠ‚ C_e(21) [i] based on
      1. linear OA(256⁵¹, 65536, F₂₅₆, 26) (dual of [65536, 65485, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      2. linear OA(256⁴³, 65536, F₂₅₆, 22) (dual of [65536, 65493, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      3. linear OA(256³, 11, F₂₅₆, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
        discarding factors / shortening the dual code based on linear OA(256³, 256, F₂₅₆, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
        Reedâ€“Solomon code RS(253,256) [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 (83, 109, 10084)-net over F₁₆	[i]		Net Duplication
2	Digital (84, 110, 10084)-net over F₁₆	[i]		Net Duplication