MinT - Information on Result #1824267

Information on Result #1824267

(79, 96, 1049599)-net in base 32, using base change based on digital (63, 80, 1049599)-net over F₆₄, using

(u,Â u+v)-construction [i] based on
1. digital (7, 15, 1024)-net over F₆₄, using
  - net defined by OOA [i] based on linear OOA(64¹⁵, 1024, F₆₄, 8, 8) (dual of [(1024, 8), 8177, 9]-NRT-code), using
    - OA 4-folding and stacking [i] based on linear OA(64¹⁵, 4096, F₆₄, 8) (dual of [4096, 4081, 9]-code), using
      - an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
2. digital (48, 65, 1048575)-net over F₆₄, using
  - net defined by OOA [i] based on linear OOA(64⁶⁵, 1048575, F₆₄, 17, 17) (dual of [(1048575, 17), 17825710, 18]-NRT-code), using
    - OOA 8-folding and stacking with additional row [i] based on linear OA(64⁶⁵, 8388601, F₆₄, 17) (dual of [8388601, 8388536, 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.

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	(80, 97, 1049599)-net in base 32	[i]		Net Duplication