MinT - Information on Result #1193462

Information on Result #1193462

Digital (77, 88, 2796208)-net over F₉, using net defined by OOA based on linear OOA(9⁸⁸, 2796208, F₉, 15, 11) (dual of [(2796208, 15), 41943032, 12]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(9⁸⁸, 5592417, F₉, 3, 11) (dual of [(5592417, 3), 16777163, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9⁸⁸, 5592418, F₉, 3, 11) (dual of [(5592418, 3), 16777166, 12]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(9⁶, 16, F₉, 3, 5) (dual of [(16, 3), 42, 6]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,42P) [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, using
        a function field by GarcÃa and Quoos [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 (165, 176, 5592416)-net over F₃	[i]		Trace Code for Nets