MinT - Information on Result #1708903

Information on Result #1708903

Linear OOA(2¹⁷⁴, 2174296, F₂, 18, 13) (dual of [(2174296, 18), 39137154, 14]-NRT-code), using OOA stacking with additional row based on linear OOA(2¹⁷⁴, 2174297, F₂, 6, 13) (dual of [(2174297, 6), 13045608, 14]-NRT-code), using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹⁷⁴, 2174297, F₂, 3, 13) (dual of [(2174297, 3), 6522717, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁷⁴, 2798248, F₂, 3, 13) (dual of [(2798248, 3), 8394570, 14]-NRT-code), using
  - 2¹ times duplication [i] based on linear OOA(2¹⁷³, 2798248, F₂, 3, 13) (dual of [(2798248, 3), 8394571, 14]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2³⁴, 2047, F₂, 3, 6) (dual of [(2047, 3), 6107, 7]-NRT-code), using
        extracting embedded OOA [i] based on digital (28, 34, 2047)-net over F₂, using
        1 times m-reduction [i] based on digital (28, 35, 2047)-net over F₂, using
        nets constructed from net-embeddable BCH codes [i]
      2. linear OOA(2¹³⁹, 2796201, F₂, 3, 13) (dual of [(2796201, 3), 8388464, 14]-NRT-code), using
        OOA 3-folding [i] based on linear OA(2¹³⁹, large, F₂, 13) (dual of [large, large−139, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Linear.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (161, 174, 2174296)-net over F₂	[i]		Net Defined by OOA