MinT - Information on Result #548072

Information on Result #548072

There is no linear OA(4¹⁰⁸, 220, F₄, 76) (dual of [220, 112, 77]-code), because constructionÂ Y1 would yield

OA(4¹⁰⁷, 141, S₄, 76), but
- the linear programming bound shows that MÂ â‰¥ 94 704083 303464 777353 653894 455864 731569 878383 755711 840806 960834 620243 478072 712366 905131 794432 / 3301 695418 882126 135009 765625 > 4¹⁰⁷ [i]
linear OA(4¹¹², 220, F₄, 79) (dual of [220, 108, 80]-code), but
- discarding factors / shortening the dual code would yield linear OA(4¹¹², 216, F₄, 79) (dual of [216, 104, 80]-code), but
  - constructionÂ Y1 [i] would yield
    1. OA(4¹¹¹, 143, S₄, 79), but
      - the linear programming bound shows that MÂ â‰¥ 237 737030 554406 831140 331461 504711 505012 046426 036658 538250 578745 045288 416863 000860 792142 692352 / 26 111742 312416 213213 385625 > 4¹¹¹ [i]
    2. OA(4¹⁰⁴, 216, S₄, 73), but
      - discarding factors would yield OA(4¹⁰⁴, 150, S₄, 73), but
        the linear programming bound shows that MÂ â‰¥ 32 028783 264027 932827 838658 827950 132017 443030 031565 779091 184319 519613 927802 631343 679332 066747 830675 439616 / 70932 376441 373736 310653 589982 582096 950125 > 4¹⁰⁴ [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OOA(4¹⁰⁸, 220, F₄, 2, 76) (dual of [(220, 2), 332, 77]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(4¹⁰⁸, 220, F₄, 3, 76) (dual of [(220, 3), 552, 77]-NRT-code)	[i]	Depth Reduction
3	No digital (32, 108, 220)-net over F₄	[i]	Extracting Embedded Orthogonal Array