Information on Result #1869630
There is no (171, 171+k, 531)-net in base 4 for arbitrarily large k, because logical equivalence would yield (171, m, 531)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (171, 2649, 531)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42649, 531, S4, 5, 2478), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 243 702749 739668 497743 599092 381242 251718 564617 792434 313214 579448 722127 742810 610858 244038 007833 309454 920686 546893 940355 636649 825689 183062 137853 961816 713646 080797 975514 611284 924601 803149 593429 045186 652987 143125 866324 252624 251097 078271 589412 785680 899034 599032 109975 273191 976026 449135 822140 091378 830158 583181 027266 746024 763174 338780 668790 384939 964881 936872 870454 475820 754027 828697 268084 550439 027577 316590 385829 703128 598557 362984 176798 725738 354689 446682 730215 986824 182278 972218 074231 283729 149171 185445 287771 920263 770760 240751 614541 420451 984468 598329 561232 006444 629750 332554 664085 934758 095413 934331 827136 198657 878929 635519 804856 179770 343945 741799 108599 850448 079664 446095 939206 640089 361005 251317 617196 632098 438304 865609 772488 337936 606256 479896 045117 373467 988284 531313 157133 606007 171090 909633 039970 662985 025388 821052 723910 667561 882539 214754 256786 277642 884677 770763 925435 466185 362133 015029 235093 415565 165486 306851 776131 056330 729686 063096 576005 993725 832058 180631 735455 624070 782936 821603 394736 854216 386694 669360 095402 174042 289414 796773 779211 594916 468691 269147 337513 711289 409943 063859 916354 562028 059172 289615 938862 975673 661740 541584 756297 004326 260046 509109 403393 409003 081180 327648 188421 381388 792999 912989 275773 902512 120031 563922 491913 675138 733249 252195 529611 280104 107024 957583 289483 043850 487399 174802 925730 381252 010063 393295 887185 936797 728410 428832 622860 387516 164520 633855 488230 735814 552675 057262 341530 423339 746540 947399 733315 126314 822785 916052 199119 353336 036335 845496 689330 818884 098556 952889 992995 158263 735898 090319 983236 726876 876295 949263 511273 592798 027363 059220 388134 991076 335522 485279 687553 732830 618003 177472 / 2479 > 42649 [i]
- extracting embedded OOA [i] would yield OOA(42649, 531, S4, 5, 2478), but
Mode: Bound.
Optimality
Show details for fixed k and s, k and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.