Information on Result #1858076
There is no (35, 965)-sequence in base 27, because net from sequence would yield (35, m, 966)-net in base 27 for arbitrarily large m, but
- m-reduction [i] would yield (35, 1929, 966)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(271929, 966, S27, 2, 1894), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5106 885089 929808 104622 457914 603717 462560 934536 577458 762597 478752 272493 524382 085746 803750 968259 201930 404234 349400 793104 720827 873636 032775 960929 533423 925228 830899 749994 996126 122011 020124 117344 730727 656221 852569 509635 971796 032317 265383 865986 989195 083674 335742 805804 674035 380926 065099 682926 536610 347832 115931 359582 991988 401871 272992 471126 107076 827499 922437 497489 145882 378870 206589 204582 946416 270187 450134 528587 040952 276428 298891 616060 372370 348374 443805 239406 712456 826896 754713 830843 688038 417771 322690 170867 724555 923090 579476 969442 950968 483897 434443 273006 501032 549295 193287 457462 903679 614684 707879 229122 395017 982006 930954 574765 710315 730860 962117 352831 175171 490650 857511 963612 089291 070439 601726 876256 491330 500384 092654 052750 630691 852085 780774 351515 601018 884660 444447 520815 074758 509811 098998 726174 966301 019021 712390 521375 258957 444291 454871 668180 129218 262940 641118 981798 061133 676897 105393 895576 053936 813093 569739 395750 982119 536185 463258 641099 456369 140449 061210 521481 322463 194920 256228 027910 258225 721949 122230 478296 376908 688813 715957 768821 114829 421671 751098 271430 805772 466825 916743 706711 974461 921698 212252 115251 332709 649128 487880 017696 457404 416852 879471 822740 790057 108678 683409 109830 113905 386804 275910 933871 973058 354089 880519 106767 149429 910666 236991 992239 027674 744177 152954 787355 670990 491943 584389 334499 866621 133079 828198 208192 718604 435420 531633 059861 201757 473166 231543 487849 436362 306880 695607 962907 903152 609185 136496 972141 937204 808010 230188 630555 523436 811910 728677 808779 245511 223103 316996 561613 143470 719424 036470 964698 930827 271080 655834 700163 716488 565031 303603 800262 729385 472572 310074 342025 734983 077133 106650 768218 910198 380559 896214 441861 811066 337122 778183 377538 623306 661237 538495 388318 320299 797005 702251 812413 641546 176818 057080 961088 576731 982065 663603 806524 776060 172901 807886 976187 775394 897219 235402 012891 686313 434151 552889 394171 568767 772178 957083 588021 850730 993234 573485 641188 137213 287615 207861 945702 645377 206953 170086 902930 966491 187059 351358 720160 123672 208363 686886 702231 954748 194370 777779 001926 790233 460846 457428 058471 919530 592801 521044 238046 630174 717457 302173 691728 892887 552213 724446 926836 755608 179211 570957 109581 521339 618714 898460 525842 752689 580203 007114 924228 780304 987554 951995 321600 257967 421827 052845 154598 871717 839536 876893 119555 822324 964355 684711 507047 621613 034299 421784 433727 803999 093184 706136 371029 006191 117945 476991 770246 747489 909223 234371 750561 378706 755640 781395 464630 048911 205948 048458 179406 842337 221600 200995 048849 789143 997281 587608 626786 085373 331989 064341 366659 573723 361639 902641 057787 156973 276149 305341 520153 278081 872561 685680 635399 581173 869897 890953 573112 821567 552316 949051 343141 791542 635015 155582 101372 093688 296556 673114 819278 268776 991041 350020 299109 001572 848982 579645 316712 172534 814231 284379 505089 334978 879325 713827 797339 639441 753510 451980 566008 811735 / 379 > 271929 [i]
- extracting embedded OOA [i] would yield OOA(271929, 966, S27, 2, 1894), 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 (35, 965)-sequence in base 27 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (35, m, 965)-net in base 27 with m > ∞ | [i] | ||
| 3 | No digital (35, 965)-sequence over F27 (for arbitrarily large k) | [i] | ||
| 4 | No digital (35, m, 965)-net over F27 with m > ∞ | [i] | ||