MinT - Information on Result #3164279

Information on Result #3164279

Digital (174, 181, large)-net over F₃, using 3 times m-reduction based on digital (174, 184, large)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (41, 46, 4194301)-net over F₃, using
  - net defined by OOA [i] based on linear OOA(3⁴⁶, 4194301, F₃, 5, 5) (dual of [(4194301, 5), 20971459, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(3⁴⁶, large, F₃, 5) (dual of [large, large−46, 6]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
2. digital (128, 138, 5033160)-net over F₃, using
  - trace code for nets [i] based on digital (36, 46, 1677720)-net over F₂₇, using
    - net defined by OOA [i] based on linear OOA(27⁴⁶, 1677720, F₂₇, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
      - OA 5-folding and stacking [i] based on linear OA(27⁴⁶, 8388600, F₂₇, 10) (dual of [8388600, 8388554, 11]-code), using
        discarding factors / shortening the dual code based on linear OA(27⁴⁶, large, F₂₇, 10) (dual of [large, large−46, 11]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 27⁵âˆ’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 t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (175, 181, large)-net over F₃	[i]		t-Expansion
2	Digital (176, 181, large)-net over F₃	[i]
3	Digital (177, 181, large)-net over F₃	[i]
4	Digital (178, 181, large)-net over F₃	[i]