MinT - Information on Result #1193366

Information on Result #1193366

Digital (77, 87, 2797820)-net over F₉, using net defined by OOA based on linear OOA(9⁸⁷, 2797820, F₉, 15, 10) (dual of [(2797820, 15), 41967213, 11]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(9⁸⁷, 5595641, F₉, 3, 10) (dual of [(5595641, 3), 16786836, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9⁸⁷, 5595642, F₉, 3, 10) (dual of [(5595642, 3), 16786839, 11]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(9¹³, 3240, F₉, 3, 5) (dual of [(3240, 3), 9707, 6]-NRT-code), using
      - OOA 2-folding and stacking with additional row [i] based on linear OA(9¹³, 6481, F₉, 5) (dual of [6481, 6468, 6]-code), using
        base reduction for projective spaces (embedding PG(6,81) in PG(12,9)) [i] based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
        a code by Danev and Olsson [i]
    2. linear OOA(9⁷⁴, 5592402, F₉, 3, 10) (dual of [(5592402, 3), 16777132, 11]-NRT-code), using
      - trace code [i] based on linear OOA(81³⁷, 2796201, F₈₁, 3, 10) (dual of [(2796201, 3), 8388566, 11]-NRT-code), using
        OOA 3-folding [i] based on linear OA(81³⁷, large, F₈₁, 10) (dual of [large, large−37, 11]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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 (164, 174, 5595640)-net over F₃	[i]		Trace Code for Nets