MinT - Information on Result #1200110

Information on Result #1200110

Digital (65, 94, 2343)-net over F₃₂, using net defined by OOA based on linear OOA(32⁹⁴, 2343, F₃₂, 29, 29) (dual of [(2343, 29), 67853, 30]-NRT-code), using

OOA 14-folding and stacking with additional row [i] based on linear OA(32⁹⁴, 32803, F₃₂, 29) (dual of [32803, 32709, 30]-code), using
- constructionÂ XX applied to C([0,14]) âŠ‚ C([0,10]) âŠ‚ C([0,9]) [i] based on
  1. linear OA(32⁸⁵, 32769, F₃₂, 29) (dual of [32769, 32684, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 32⁶âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
  2. linear OA(32⁶¹, 32769, F₃₂, 21) (dual of [32769, 32708, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 32⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
  3. linear OA(32⁵⁵, 32769, F₃₂, 19) (dual of [32769, 32714, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 32⁶âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
  4. linear OA(32⁷, 32, F₃₂, 7) (dual of [32, 25, 8]-code or 32-arc in PG(6,32)), using
    - Reedâ€“Solomon code RS(25,32) [i]
  5. linear OA(32¹, 2, F₃₂, 1) (dual of [2, 1, 2]-code), using
    - dual of repetition code with length 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 (66, 94, 2343)-net over F₃₂	[i]	t-Expansion
2	Digital (66, 95, 2343)-net over F₃₂	[i]	Net Duplication
3	Digital (67, 96, 2343)-net over F₃₂	[i]
4	Digital (68, 97, 2343)-net over F₃₂	[i]
5	Digital (69, 98, 2343)-net over F₃₂	[i]
6	Digital (65, 93, 2343)-net over F₃₂	[i]	m-Reduction