MinT - Information on Result #1200932

Information on Result #1200932

Digital (13, 20, 87384)-net over F₆₄, using net defined by OOA based on linear OOA(64²⁰, 87384, F₆₄, 7, 7) (dual of [(87384, 7), 611668, 8]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OA(64²⁰, 262153, F₆₄, 7) (dual of [262153, 262133, 8]-code), using
- constructionÂ X4 applied to C([0,3]) âŠ‚ C([0,2]) [i] based on
  1. linear OA(64¹⁹, 262145, F₆₄, 7) (dual of [262145, 262126, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
  2. linear OA(64¹³, 262145, F₆₄, 5) (dual of [262145, 262132, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
  3. linear OA(64⁷, 8, F₆₄, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,64)), using
    - dual of repetition code with length 8 [i]
  4. linear OA(64¹, 8, F₆₄, 1) (dual of [8, 7, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(64¹, 64, F₆₄, 1) (dual of [64, 63, 2]-code), using
      - Reedâ€“Solomon code RS(63,64) [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 (14, 21, 87384)-net over F₆₄	[i]	Net Duplication
2	Digital (59, 73, 1285755)-net over F₆₄	[i]	(u,Â u+v)-Construction for Nets
3	Digital (62, 77, 1285755)-net over F₆₄	[i]	(u,Â u+v)-Construction for Nets
4	Digital (27, 34, 5592576)-net over F₆₄	[i]	Generalized (u,Â u+v)-Construction for Nets
5	(17, 24, 87384)-net in base 32	[i]	Base Change
6	(23, 30, 87384)-net in base 16	[i]	Base Change