MinT - Information on Result #1201174

Information on Result #1201174

Digital (22, 34, 43691)-net over F₆₄, using net defined by OOA based on linear OOA(64³⁴, 43691, F₆₄, 12, 12) (dual of [(43691, 12), 524258, 13]-NRT-code), using

OA 6-folding and stacking [i] based on linear OA(64³⁴, 262146, F₆₄, 12) (dual of [262146, 262112, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(64³⁴, 262147, F₆₄, 12) (dual of [262147, 262113, 13]-code), using
  - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
    1. linear OA(64³⁴, 262144, F₆₄, 12) (dual of [262144, 262110, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
    2. linear OA(64³¹, 262144, F₆₄, 11) (dual of [262144, 262113, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
    3. linear OA(64⁰, 3, F₆₄, 0) (dual of [3, 3, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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 (23, 35, 43691)-net over F₆₄	[i]	Net Duplication
2	Digital (28, 40, 43756)-net over F₆₄	[i]	(u,Â u+v)-Construction for Nets
3	Digital (29, 41, 43771)-net over F₆₄	[i]
4	Digital (31, 43, 43821)-net over F₆₄	[i]
5	Digital (32, 44, 43836)-net over F₆₄	[i]
6	(39, 51, 43691)-net in base 16	[i]	Base Change