MinT - Information on Result #1201470

Information on Result #1201470

Digital (57, 73, 1048607)-net over F₆₄, using net defined by OOA based on linear OOA(64⁷³, 1048607, F₆₄, 18, 16) (dual of [(1048607, 18), 18874853, 17]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(64⁷³, 4194429, F₆₄, 2, 16) (dual of [(4194429, 2), 8388785, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(64⁷³, 4194431, F₆₄, 2, 16) (dual of [(4194431, 2), 8388789, 17]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(64¹², 130, F₆₄, 2, 8) (dual of [(130, 2), 248, 9]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(64⁴, 65, F₆₄, 2, 4) (dual of [(65, 2), 126, 5]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;126,64) [i]
        linear OOA(64⁸, 65, F₆₄, 2, 8) (dual of [(65, 2), 122, 9]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;122,64) [i]
    2. linear OOA(64⁶¹, 4194301, F₆₄, 2, 16) (dual of [(4194301, 2), 8388541, 17]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(64⁶¹, 8388602, F₆₄, 16) (dual of [8388602, 8388541, 17]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁶¹, large, F₆₄, 16) (dual of [large, large−61, 17]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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 (130, 146, 2097214)-net over F₈	[i]		Trace Code for Nets