Information on Result #1854222
There is no (23, m, 653)-net in base 27 for arbitrarily large m, because m-reduction would yield (23, 1303, 653)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(271303, 653, S27, 2, 1280), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 61 955407 846462 017289 314627 903423 099165 842394 578318 909544 435022 710857 589875 764029 057314 799001 372741 943202 578220 078344 470861 245832 172851 334750 052515 591892 918650 955228 311787 819496 883959 292435 726507 633027 839736 240393 602103 436263 541152 114271 684005 437875 940281 653328 073413 485461 150194 192197 555827 618949 068403 380556 402962 982554 079193 045479 375746 747065 813654 851064 797920 703821 016647 115077 967972 115142 980943 666401 443000 594752 177856 018990 355498 914878 480961 092650 571943 015838 619208 807308 365319 497480 866116 621545 081654 835101 058720 900458 822833 633364 901050 653927 208266 066313 245328 964327 051651 597105 303955 236324 010800 486743 323753 670262 347708 910006 620606 899653 261437 807538 628904 322434 922016 968606 813103 610618 759597 069002 241395 560909 989464 504619 690234 011105 601155 284380 386133 199700 020092 149409 086175 519916 238183 981968 078022 476746 881457 157468 492475 954379 128634 294188 856375 001122 175558 190211 533681 544833 446459 741582 531753 375082 527781 923234 100899 503496 768344 630573 917360 863152 729965 989427 188631 143305 132134 571555 363346 263129 781847 065985 445468 646704 108691 845083 021827 940053 930974 810754 449671 452004 381645 830688 885109 743676 275215 287252 520852 525747 392840 991057 857669 093029 276333 038587 230693 755020 419986 734385 624794 084036 371348 354071 262689 225526 358088 322910 004603 105973 920230 465755 074651 337586 471371 919222 549812 591993 625708 418326 681357 825682 603814 432634 153461 703564 441145 929886 800763 690927 804832 820549 356583 141449 367113 872051 335863 721759 639538 059266 078589 841192 840272 346308 472712 931549 183157 207276 725544 408807 876390 005094 454483 169607 422903 898661 240580 886348 590110 061842 073203 773295 793929 216750 502705 724324 957874 259769 503106 275033 800387 569820 720163 943432 272232 999053 036067 063086 608596 372013 235394 549069 777151 169764 761855 116781 558426 138707 097850 059992 949168 610752 985455 627332 669668 203862 046846 170960 907845 345716 193041 580158 729502 004189 574617 773098 833641 210072 170285 209552 692123 238222 408010 385673 / 427 > 271303 [i]
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 (23, 652)-sequence in base 27 | [i] | Net from Sequence | |
| 2 | No (23, 23+k, 653)-net in base 27 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (23, m, 653)-net in base 27 with unbounded m | [i] | ||
| 4 | No digital (23, 23+k, 653)-net over F27 for arbitrarily large k | [i] | ||
| 5 | No digital (23, m, 653)-net over F27 with unbounded m | [i] | ||