MinT - Information on Result #1201548

Information on Result #1201548

Digital (60, 77, 1048607)-net over F₆₄, using net defined by OOA based on linear OOA(64⁷⁷, 1048607, F₆₄, 18, 17) (dual of [(1048607, 18), 18874849, 18]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(64⁷⁷, 4194429, F₆₄, 2, 17) (dual of [(4194429, 2), 8388781, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(64⁷⁷, 4194431, F₆₄, 2, 17) (dual of [(4194431, 2), 8388785, 18]-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(64⁶⁵, 4194301, F₆₄, 2, 17) (dual of [(4194301, 2), 8388537, 18]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(64⁶⁵, 8388602, F₆₄, 17) (dual of [8388602, 8388537, 18]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁶⁵, large, F₆₄, 17) (dual of [large, large−65, 18]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [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 (137, 154, 2097214)-net over F₈	[i]		Trace Code for Nets