MinT - Information on Result #1215207

Information on Result #1215207

Digital (133, 144, large)-net over F₈, using (u,Â u+v)-construction based on

digital (28, 33, 4194301)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8³³, 4194301, F₈, 5, 5) (dual of [(4194301, 5), 20971472, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(8³³, large, F₈, 5) (dual of [large, large−33, 6]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 8¹⁶âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
digital (100, 111, 4404019)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (24, 29, 1048579)-net over F₈, using
    - net defined by OOA [i] based on linear OOA(8²⁹, 1048579, F₈, 5, 5) (dual of [(1048579, 5), 5242866, 6]-NRT-code), using
      - OOA 2-folding and stacking with additional row [i] based on linear OA(8²⁹, 2097159, F₈, 5) (dual of [2097159, 2097130, 6]-code), using
        constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
        linear OA(8²⁹, 2097152, F₈, 5) (dual of [2097152, 2097123, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(8²², 2097152, F₈, 4) (dual of [2097152, 2097130, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(8⁰, 7, F₈, 0) (dual of [7, 7, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
  2. digital (71, 82, 3355440)-net over F₈, using
    - trace code for nets [i] based on digital (30, 41, 1677720)-net over F₆₄, using
      - net defined by OOA [i] based on linear OOA(64⁴¹, 1677720, F₆₄, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
        OOA 5-folding and stacking with additional row [i] based on linear OA(64⁴¹, 8388601, F₆₄, 11) (dual of [8388601, 8388560, 12]-code), using
        discarding factors / shortening the dual code 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 t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Digital (134, 144, large)-net over F₈	[i]	t-Expansion
2	Digital (135, 144, large)-net over F₈	[i]
3	Digital (136, 144, large)-net over F₈	[i]
4	Digital (137, 144, large)-net over F₈	[i]
5	Digital (138, 144, large)-net over F₈	[i]
6	Digital (139, 144, large)-net over F₈	[i]
7	Digital (140, 144, large)-net over F₈	[i]
8	Digital (141, 144, large)-net over F₈	[i]
9	Digital (134, 145, large)-net over F₈	[i]	Net Duplication
10	Digital (135, 146, large)-net over F₈	[i]
11	Digital (136, 147, large)-net over F₈	[i]
12	Digital (137, 148, large)-net over F₈	[i]
13	Digital (138, 149, large)-net over F₈	[i]
14	Digital (139, 150, large)-net over F₈	[i]
15	Digital (140, 151, large)-net over F₈	[i]
16	Digital (141, 152, large)-net over F₈	[i]
17	Digital (142, 153, large)-net over F₈	[i]
18	Digital (143, 154, large)-net over F₈	[i]
19	Digital (144, 155, large)-net over F₈	[i]
20	Digital (145, 156, large)-net over F₈	[i]
21	Digital (146, 157, large)-net over F₈	[i]
22	Digital (133, 143, large)-net over F₈	[i]	m-Reduction
23	Digital (133, 142, large)-net over F₈	[i]
24	Digital (133, 141, large)-net over F₈	[i]
25	Digital (133, 140, large)-net over F₈	[i]
26	Digital (133, 139, large)-net over F₈	[i]
27	Digital (133, 138, large)-net over F₈	[i]
28	Digital (133, 137, large)-net over F₈	[i]
29	Digital (133, 136, large)-net over F₈	[i]