MinT - Information on Result #599837

Information on Result #599837

There is no digital (19, 129, 230)-net over F₈, because extracting embedded orthogonal array would yield linear OA(8¹²⁹, 230, F₈, 110) (dual of [230, 101, 111]-code), but

constructionÂ Y1 [i] would yield
1. OA(8¹²⁸, 144, S₈, 110), but
  - the linear programming bound shows that MÂ â‰¥ 6109 893966 434273 613815 828543 318095 703793 603744 881950 919851 825987 742070 359262 466307 770153 217353 472069 496822 008994 926770 763501 404160 / 124 535855 141787 > 8¹²⁸ [i]
2. OA(8¹⁰¹, 230, S₈, 86), but
  - discarding factors would yield OA(8¹⁰¹, 146, S₈, 86), but
    - the linear programming bound shows that MÂ â‰¥ 47452 756982 762840 644180 785646 906838 805374 098587 752364 011747 551574 239635 502216 492748 447610 784265 998302 557863 887131 929643 838881 370395 949171 355783 528448 / 2798 356661 117080 828757 255676 140575 034437 993397 485091 746485 > 8¹⁰¹ [i]

Mode: Bound (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	No digital (19, 130, 230)-net over F₈	[i]	m-Reduction
2	No digital (19, 131, 230)-net over F₈	[i]
3	No digital (19, 132, 230)-net over F₈	[i]
4	No digital (19, 133, 230)-net over F₈	[i]
5	No digital (19, 134, 230)-net over F₈	[i]
6	No digital (19, 135, 230)-net over F₈	[i]
7	No digital (19, 136, 230)-net over F₈	[i]
8	No digital (19, 137, 230)-net over F₈	[i]
9	No digital (19, 138, 230)-net over F₈	[i]