Information on Result #1880436
There is no digital (71, 71+k, 595)-net over F9 for arbitrarily large k, because logical equivalence would yield (71, m, 595)-net in base 9 for arbitrarily large m, but
- m-reduction [i] would yield (71, 1781, 595)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(91781, 595, S9, 3, 1710), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 57412 293622 172545 682256 216657 415398 728369 598617 468883 521827 833990 593824 510885 349319 960795 000430 562731 317386 784015 947825 856212 423093 564107 558519 708619 884208 953446 206718 041421 722002 469550 224920 157724 729289 019235 848732 703571 535585 977116 531503 611496 896031 234207 316100 534190 607415 454640 607616 735054 754822 776012 487281 132891 330824 600905 324514 797773 793437 436480 401757 952144 760024 020881 101797 338927 245556 201104 356435 708015 652576 597216 952645 112887 790837 749369 923192 461972 396984 881213 464441 664246 423389 197901 388446 976631 811211 204607 551072 895400 091766 676001 631690 735686 988858 189111 113108 690265 236561 133893 746285 774430 441777 671273 939136 069361 669307 930997 003841 079482 270947 354298 452620 230641 571449 527680 396930 872514 549070 846094 850217 894392 623921 438321 133034 345888 060419 832368 920920 994668 636597 080860 297432 034775 834766 742170 631619 989829 993263 192469 592646 498825 461945 374100 708525 121689 079552 608662 720527 800741 785809 406715 043026 701320 243044 504319 093137 692259 958335 109948 386912 681538 732186 606410 008671 297235 026870 163578 541272 625130 728522 347633 380001 302168 421209 596363 894690 076560 495234 167147 280191 151224 838178 482846 247495 535385 386660 986360 420464 013879 636840 461892 915060 715034 286495 970875 824300 029696 480187 519501 269589 297489 166544 249652 829034 663790 364579 388545 316557 180718 687879 243645 491235 456712 654109 992683 488076 902813 674054 856937 121779 590608 814052 220200 590587 342987 622087 637840 828800 239507 461362 407980 569695 913781 722158 026039 911165 502363 139941 288456 694385 272649 262383 037816 165355 764496 922301 541765 563123 489934 114036 267838 315758 800562 105483 761753 583321 381756 984170 771243 141734 113077 264313 365488 197726 939447 900733 715009 598691 660046 233754 333846 976786 265255 084560 381197 098411 670738 644881 421579 088154 877738 314060 498853 896919 / 1711 > 91781 [i]
- extracting embedded OOA [i] would yield OOA(91781, 595, S9, 3, 1710), but
Mode: Bound (linear).
Optimality
Show details for fixed k and s, k and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.