MinT - Information on Result #1857328

Information on Result #1857328

There is no (65, 412)-sequence in base 7, because net from sequence would yield (65, m, 413)-net in base 7 for arbitrarily large m, but

m-reduction [i] would yield (65, 1235, 413)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7¹²³⁵, 413, S₇, 3, 1170), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 754 461688 908392 843516 032160 139558 112805 778935 067483 754978 302004 686673 201260 143390 910877 829389 971610 550384 112517 639774 850488 348701 899315 056960 442455 466493 555922 591574 971645 586666 320354 078803 389934 190830 527683 758021 830249 674170 430069 246897 886321 388455 399224 212668 200684 590529 921885 562595 673072 262165 517156 131533 537963 640873 783557 745545 866581 520332 542146 281483 326532 883755 586873 047742 026783 268327 398244 764963 921747 598659 218474 237217 973702 050629 294968 643248 729967 051289 933734 161167 557676 265946 421914 035410 938930 370326 895585 316801 610110 993240 423790 916483 727684 374513 270747 913485 587826 232009 696058 436715 444263 037990 485799 018670 583493 318662 976828 561818 606324 474609 437016 995230 468158 844728 145861 044478 753389 942057 210788 780537 270995 278875 584270 528139 853970 706974 657808 363088 181343 249549 481588 474495 598191 632213 712833 040158 065357 546053 128973 659934 275283 469249 432629 596565 756861 374866 940467 848057 112996 911384 350409 296270 447414 349636 114179 356182 172205 474777 350729 902576 435234 366952 304837 157864 961955 861713 560163 148409 200489 845805 824579 687555 937691 328326 047417 / 1171 > 7¹²³⁵ [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 (65, 412)-sequence in base 7 (for arbitrarily large k)	[i]	Logical Equivalence (for Sequences)
2	No (65, m, 412)-net in base 7 with m > ∞	[i]
3	No digital (65, 412)-sequence over F₇ (for arbitrarily large k)	[i]
4	No digital (65, m, 412)-net over F₇ with m > ∞	[i]