Information on Result #1857086
There is no (235, 723)-sequence in base 4, because net from sequence would yield (235, m, 724)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (235, 3614, 724)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43614, 724, S4, 5, 3379), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 7 862759 110443 082943 934214 808224 623398 450339 146013 373483 622146 135267 165400 150614 722178 977186 331654 212762 483169 243397 103651 431181 948253 451959 365985 364641 138167 979988 764525 882045 269112 628453 973645 563127 446853 098117 456189 101145 314993 222979 472248 580001 603880 218916 338488 595665 100015 972185 738159 352645 509224 691384 823181 945427 678420 994659 463533 074611 641909 341976 430265 273362 938654 737286 044239 762300 269535 976602 210472 948863 039162 913010 403904 596755 422279 540301 761271 737823 532804 470404 411881 280594 308631 618132 344468 761434 439762 589265 737018 011693 474893 185023 226138 263285 028388 186196 255987 989776 226585 908181 512896 302645 465515 736168 225342 371257 358341 291102 682433 624463 603795 181487 240985 889069 532515 123963 504307 772801 665869 018423 769227 666775 243558 191483 392391 405592 535046 932736 142248 461685 375819 744705 345750 431079 965748 742636 181803 890433 549603 737798 711407 810732 371706 598317 325837 517201 374177 522373 244635 003788 955080 665681 945879 732297 294876 021838 234254 603624 442521 884389 106069 937902 028665 678401 058449 931592 964159 147509 015220 568615 100185 140383 612361 989918 426606 456903 845548 079484 435806 890959 434991 556491 725438 280530 816865 359991 197820 305269 114433 411111 091423 021830 130237 801165 093311 638596 778123 178775 144314 165515 094584 259670 800306 098155 923191 268696 846098 011104 444706 267555 437946 396172 624727 784140 527454 582805 479714 780513 158292 916427 909913 617559 086237 357371 720727 264689 006063 721519 602087 330134 505444 255172 761937 498948 384978 451844 633435 749081 753501 672626 059060 119060 835736 100031 465285 819600 711764 169348 730386 867588 123767 608691 442620 601250 011973 035222 238781 972025 096986 678861 083861 029160 039743 655227 161879 619635 976750 384200 023189 865543 911812 025096 650194 584952 608645 000810 829210 650633 829848 579111 551053 293766 610512 544390 162210 854577 542024 217931 540526 398351 599493 401123 779538 950735 399094 187115 716411 113558 996815 927113 826048 383673 274192 293969 642279 127209 170570 691258 730193 419806 657724 113508 074310 196498 137032 763757 302877 753126 387921 922365 440281 735583 387658 399973 336516 525331 122221 369073 130771 064860 419063 985740 165501 714853 483941 709626 882866 236083 531513 070137 665502 471920 300978 597328 380124 139947 445212 546536 329121 634042 389043 239066 084249 697731 332840 306672 849539 880024 945638 315042 937441 079628 991817 580544 / 845 > 43614 [i]
- extracting embedded OOA [i] would yield OOA(43614, 724, S4, 5, 3379), but
Mode: Bound.
Optimality
Show details for fixed 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 | This result only | Method | ||
|---|---|---|---|---|
| 1 | No (235, 723)-sequence in base 4 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (235, m, 723)-net in base 4 with m > ∞ | [i] | ||
| 3 | No digital (235, 723)-sequence over F4 (for arbitrarily large k) | [i] | ||
| 4 | No digital (235, m, 723)-net over F4 with m > ∞ | [i] | ||