MinT - Information on Result #3211013

Information on Result #3211013

Digital (163, 171, large)-net over F₄, using t-expansion based on digital (161, 171, large)-net over F₄, using

trace code for nets [i] based on digital (47, 57, 2796233)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64⁵⁷, 2796233, F₆₄, 15, 10) (dual of [(2796233, 15), 41943438, 11]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OOA(64⁵⁷, 5592467, F₆₄, 3, 10) (dual of [(5592467, 3), 16777344, 11]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(64³, 65, F₆₄, 3, 3) (dual of [(65, 3), 192, 4]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;192,64) [i]
      2. linear OOA(64¹⁷, 2796201, F₆₄, 3, 5) (dual of [(2796201, 3), 8388586, 6]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(64¹⁷, 4194301, F₆₄, 3, 5) (dual of [(4194301, 3), 12582886, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(64¹⁷, large, F₆₄, 5) (dual of [large, large−17, 6]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
      3. linear OOA(64³⁷, 2796201, F₆₄, 3, 10) (dual of [(2796201, 3), 8388566, 11]-NRT-code), using
        OOA 3-folding [i] based on linear OA(64³⁷, large, F₆₄, 10) (dual of [large, large−37, 11]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’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 (164, 172, large)-net over F₄	[i]		Net Duplication