MinT - Information on Result #548074

Information on Result #548074

There is no linear OA(4¹¹⁴, 229, F₄, 80) (dual of [229, 115, 81]-code), because constructionÂ Y1 would yield

OA(4¹¹³, 148, S₄, 80), but
- the linear programming bound shows that MÂ â‰¥ 134390 122763 442072 744489 280693 386578 084491 173770 590049 483300 612364 941999 081453 236362 093214 564352 / 1168 599339 892305 226318 359375 > 4¹¹³ [i]
linear OA(4¹¹⁵, 229, F₄, 81) (dual of [229, 114, 82]-code), but
- discarding factors / shortening the dual code would yield linear OA(4¹¹⁵, 219, F₄, 81) (dual of [219, 104, 82]-code), but
  - constructionÂ Y1 [i] would yield
    1. OA(4¹¹⁴, 146, S₄, 81), but
      - the linear programming bound shows that MÂ â‰¥ 7 594596 073360 304072 815867 736592 315637 386549 140598 576996 791410 829396 630589 236390 143121 686528 / 15336 256272 900153 260065 > 4¹¹⁴ [i]
    2. OA(4¹⁰⁴, 219, 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(4¹¹⁴, 229, F₄, 2, 80) (dual of [(229, 2), 344, 81]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(4¹¹⁴, 229, F₄, 3, 80) (dual of [(229, 3), 573, 81]-NRT-code)	[i]	Depth Reduction
3	No digital (34, 114, 229)-net over F₄	[i]	Extracting Embedded Orthogonal Array