MinT - Information on Result #1824239

Information on Result #1824239

(69, 84, 1199736)-net in base 32, using base change based on digital (55, 70, 1199736)-net over F₆₄, using

(u,Â u+v)-construction [i] based on
1. digital (6, 13, 1365)-net over F₆₄, using
  - net defined by OOA [i] based on linear OOA(64¹³, 1365, F₆₄, 7, 7) (dual of [(1365, 7), 9542, 8]-NRT-code), using
    - OOA 3-folding and stacking with additional row [i] based on linear OA(64¹³, 4096, F₆₄, 7) (dual of [4096, 4083, 8]-code), using
      - an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
2. digital (42, 57, 1198371)-net over F₆₄, using
  - net defined by OOA [i] based on linear OOA(64⁵⁷, 1198371, F₆₄, 15, 15) (dual of [(1198371, 15), 17975508, 16]-NRT-code), using
    - OOA 7-folding and stacking with additional row [i] based on linear OA(64⁵⁷, 8388598, F₆₄, 15) (dual of [8388598, 8388541, 16]-code), using
      - discarding factors / shortening the dual code based on linear OA(64⁵⁷, large, F₆₄, 15) (dual of [large, large−57, 16]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]

Mode: Constructive.

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	(70, 85, 1199736)-net in base 32	[i]		Net Duplication