MinT - Information on Result #1193718

Information on Result #1193718

Digital (93, 106, 2796210)-net over F₉, using net defined by OOA based on linear OOA(9¹⁰⁶, 2796210, F₉, 15, 13) (dual of [(2796210, 15), 41943044, 14]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(9¹⁰⁶, 5592421, F₉, 3, 13) (dual of [(5592421, 3), 16777157, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9¹⁰⁶, 5592422, F₉, 3, 13) (dual of [(5592422, 3), 16777160, 14]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(9⁸, 20, F₉, 3, 6) (dual of [(20, 3), 52, 7]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,53P) [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
        a function field by GarcÃa and Quoos [i]
    2. linear OOA(9⁹⁸, 5592402, F₉, 3, 13) (dual of [(5592402, 3), 16777108, 14]-NRT-code), using
      - trace code [i] based on linear OOA(81⁴⁹, 2796201, F₈₁, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
        OOA 3-folding [i] based on linear OA(81⁴⁹, large, F₈₁, 13) (dual of [large, large−49, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’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		This result only	Method
1	Digital (199, 212, 5592420)-net over F₃	[i]		Trace Code for Nets