MinT - Information on Result #3277090

Information on Result #3277090

(46, 72, 505)-net in base 27, using t-expansion based on (45, 72, 505)-net in base 27, using

base change [i] based on digital (27, 54, 505)-net over F₈₁, using
- net defined by OOA [i] based on linear OOA(81⁵⁴, 505, F₈₁, 27, 27) (dual of [(505, 27), 13581, 28]-NRT-code), using
  - OOA 13-folding and stacking with additional row [i] based on linear OA(81⁵⁴, 6566, F₈₁, 27) (dual of [6566, 6512, 28]-code), using
    - discarding factors / shortening the dual code based on linear OA(81⁵⁴, 6567, F₈₁, 27) (dual of [6567, 6513, 28]-code), using
      - constructionÂ X applied to C([0,13]) âŠ‚ C([0,12]) [i] based on
        linear OA(81⁵³, 6562, F₈₁, 27) (dual of [6562, 6509, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
        linear OA(81⁴⁹, 6562, F₈₁, 25) (dual of [6562, 6513, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
        linear OA(81¹, 5, F₈₁, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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	(47, 73, 505)-net in base 27	[i]		Net Duplication
2	(48, 74, 505)-net in base 27	[i]		Net Duplication