MinT - Information on Result #1201156

Information on Result #1201156

Digital (54, 65, 4194301)-net over F₆₄, using net defined by OOA based on linear OOA(64⁶⁵, 4194301, F₆₄, 15, 11) (dual of [(4194301, 15), 62914450, 12]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(64⁶⁵, large, F₆₄, 3, 11), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(64⁷, 2796201, F₆₄, 3, 3) (dual of [(2796201, 3), 8388596, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁷, 8388602, F₆₄, 3, 3) (dual of [(8388602, 3), 25165799, 4]-NRT-code), using
      - OOA stacking with additional row [i] based on linear OA(64⁷, large, F₆₄, 3) (dual of [large, large−7, 4]-code), using
        product of projective cap with 64²-ovoid cap in AG(3,Â 64) [i] based on linear OA(64⁴, 4097, F₆₄, 3) (dual of [4097, 4093, 4]-code or 4097-cap in PG(3,64)), using
        ovoid in PG(3,Â 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(64⁴¹, 2796201, F₆₄, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(64⁴¹, large, F₆₄, 11) (dual of [large, large−41, 12]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (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		Method
1	Digital (119, 130, 8388602)-net over F₈	[i]	Trace Code for Nets
2	Digital (59, 70, 4194366)-net over F₆₄	[i]	(u,Â u+v)-Construction for Nets
3	Digital (60, 71, 4194381)-net over F₆₄	[i]
4	Digital (61, 72, 4196317)-net over F₆₄	[i]
5	Digital (63, 74, 4196382)-net over F₆₄	[i]
6	Digital (71, 82, 8388602)-net over F₆₄	[i]