MinT - Information on Result #1182718

Information on Result #1182718

Digital (214, 247, 2050)-net over F₂, using net defined by OOA based on linear OOA(2²⁴⁷, 2050, F₂, 33, 33) (dual of [(2050, 33), 67403, 34]-NRT-code), using

OOA 16-folding and stacking with additional row [i] based on linear OA(2²⁴⁷, 32801, F₂, 33) (dual of [32801, 32554, 34]-code), using
- constructionÂ X applied to C([0,16]) âŠ‚ C([0,14]) [i] based on
  1. linear OA(2²⁴¹, 32769, F₂, 33) (dual of [32769, 32528, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 2³⁰âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]
  2. linear OA(2²¹¹, 32769, F₂, 29) (dual of [32769, 32558, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 2³⁰âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
  3. linear OA(2⁶, 32, F₂, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
    - Reedâ€“Muller code RM(1,5) [i]
    - caps in base bÂ =Â 2 [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 (215, 247, 2050)-net over F₂	[i]	t-Expansion
2	Digital (215, 248, 2050)-net over F₂	[i]	Net Duplication
3	Digital (216, 249, 2050)-net over F₂	[i]
4	Digital (217, 250, 2050)-net over F₂	[i]
5	Digital (218, 251, 2050)-net over F₂	[i]
6	Digital (219, 252, 2050)-net over F₂	[i]
7	Digital (220, 253, 2050)-net over F₂	[i]