MinT - Information on Result #1199292

Information on Result #1199292

Digital (74, 87, 2796200)-net over F₃₂, using net defined by OOA based on linear OOA(32⁸⁷, 2796200, F₃₂, 14, 13) (dual of [(2796200, 14), 39146713, 14]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(32⁸⁷, 8388601, F₃₂, 2, 13) (dual of [(8388601, 2), 16777115, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(32⁸⁷, 8388602, F₃₂, 2, 13) (dual of [(8388602, 2), 16777117, 14]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(32²⁶, 4194301, F₃₂, 2, 6) (dual of [(4194301, 2), 8388576, 7]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(32²⁶, 8388602, F₃₂, 6) (dual of [8388602, 8388576, 7]-code), using
        discarding factors / shortening the dual code based on linear OA(32²⁶, large, F₃₂, 6) (dual of [large, large−26, 7]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 33554431Â = 32⁵âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    2. linear OOA(32⁶¹, 4194301, F₃₂, 2, 13) (dual of [(4194301, 2), 8388541, 14]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(32⁶¹, 8388602, F₃₂, 13) (dual of [8388602, 8388541, 14]-code), using
        discarding factors / shortening the dual code based on linear OA(32⁶¹, large, F₃₂, 13) (dual of [large, large−61, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 33554433Â | 32¹⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [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 (75, 88, 2796200)-net over F₃₂	[i]	Net Duplication
2	Digital (76, 89, 2796200)-net over F₃₂	[i]
3	Digital (77, 90, 2796200)-net over F₃₂	[i]