MinT - Information on Result #1193464

Information on Result #1193464

Digital (78, 89, 2796218)-net over F₉, using net defined by OOA based on linear OOA(9⁸⁹, 2796218, F₉, 15, 11) (dual of [(2796218, 15), 41943181, 12]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(9⁸⁹, 5592437, F₉, 3, 11) (dual of [(5592437, 3), 16777222, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9⁸⁹, 5592438, F₉, 3, 11) (dual of [(5592438, 3), 16777225, 12]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(9⁷, 36, F₉, 3, 5) (dual of [(36, 3), 101, 6]-NRT-code), using
      - OOA 2-folding and stacking with additional row [i] based on linear OA(9⁷, 73, F₉, 5) (dual of [73, 66, 6]-code), using
        a code by Danev and Olsson [i]
    2. linear OOA(9⁸², 5592402, F₉, 3, 11) (dual of [(5592402, 3), 16777124, 12]-NRT-code), using
      - trace code [i] based on linear OOA(81⁴¹, 2796201, F₈₁, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
        OOA 3-folding [i] based on linear OA(81⁴¹, large, F₈₁, 11) (dual of [large, large−41, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (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		This result only	Method
1	Digital (167, 178, 5592436)-net over F₃	[i]		Trace Code for Nets