MinT - Information on Result #3168512

Information on Result #3168512

Digital (206, 212, large)-net over F₄, using 7 times m-reduction based on digital (206, 219, large)-net over F₄, using

trace code for nets [i] based on digital (60, 73, 2796201)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64⁷³, 2796201, F₆₄, 15, 13) (dual of [(2796201, 15), 41942942, 14]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OOA(64⁷³, 5592403, F₆₄, 3, 13) (dual of [(5592403, 3), 16777136, 14]-NRT-code), using
    - 1 times NRT-code embedding in larger space [i] based on linear OOA(64⁷⁰, 5592402, F₆₄, 3, 13) (dual of [(5592402, 3), 16777136, 14]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(64²¹, 2796201, F₆₄, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
        OOA 3-folding [i] based on linear OA(64²¹, large, F₆₄, 6) (dual of [large, large−21, 7]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OOA(64⁴⁹, 2796201, F₆₄, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
        OOA 3-folding [i] based on linear OA(64⁴⁹, large, F₆₄, 13) (dual of [large, large−49, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’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 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 (207, 212, large)-net over F₄	[i]		t-Expansion
2	Digital (208, 212, large)-net over F₄	[i]
3	Digital (209, 212, large)-net over F₄	[i]