MinT - Information on Result #1856906

Information on Result #1856906

There is no (55, 179)-sequence in base 4, because net from sequence would yield (55, m, 180)-net in base 4 for arbitrarily large m, but

m-reduction [i] would yield (55, 715, 180)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4⁷¹⁵, 180, S₄, 4, 660), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 23 292165 226338 150497 413837 680749 468165 158064 818907 090678 280277 145093 831671 774801 570450 532309 408343 381370 778690 973470 702023 045705 361421 179050 557263 352433 855467 757534 777884 032434 483025 797135 401934 632090 244028 777349 464485 685605 081042 699734 979180 059788 898455 170515 848758 719151 351344 977588 846016 713656 209655 862263 184840 537771 817665 060935 803432 767334 671398 366933 206983 571478 392544 010283 372701 995731 294508 790281 913243 365906 085225 962475 094016 / 661 > 4⁷¹⁵ [i]

Mode: Bound.

Show details for fixed m and s, m and t, t and s.

None.

The following results depend on this result:

	Result		Method
1	No (55, 179)-sequence in base 4 (for arbitrarily large k)	[i]	Logical Equivalence (for Sequences)
2	No (55, m, 179)-net in base 4 with m > ∞	[i]
3	No digital (55, 179)-sequence over F₄ (for arbitrarily large k)	[i]
4	No digital (55, m, 179)-net over F₄ with m > ∞	[i]