MinT - Information on Result #1825175

Information on Result #1825175

(38, 60, 597)-net in base 27, using base change based on digital (23, 45, 597)-net over F₈₁, using

net defined by OOA [i] based on linear OOA(81⁴⁵, 597, F₈₁, 22, 22) (dual of [(597, 22), 13089, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(81⁴⁵, 6567, F₈₁, 22) (dual of [6567, 6522, 23]-code), using
  - discarding factors / shortening the dual code based on linear OA(81⁴⁵, 6569, F₈₁, 22) (dual of [6569, 6524, 23]-code), using
    - constructionÂ X applied to C_e(21) âŠ‚ C_e(18) [i] based on
      1. linear OA(81⁴³, 6561, F₈₁, 22) (dual of [6561, 6518, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      2. linear OA(81³⁷, 6561, F₈₁, 19) (dual of [6561, 6524, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      3. linear OA(81², 8, F₈₁, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,81)), using
        discarding factors / shortening the dual code based on linear OA(81², 81, F₈₁, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
        Reedâ€“Solomon code RS(79,81) [i]

Mode: Constructive.

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	(39, 61, 597)-net in base 27	[i]		Net Duplication