Information on Result #1877359
There is no digital (12, m, 1066)-net over F81 with m > ∞, because logical equivalence would yield (12, 1066)-sequence in base 81, but
- net from sequence [i] would yield (12, m, 1067)-net in base 81 for arbitrarily large m, but
- m-reduction [i] would yield (12, 1065, 1067)-net in base 81, but
- extracting embedded OOA [i] would yield OA(811065, 1067, S81, 1053), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 19 504201 033585 446471 999444 810946 592852 085131 581967 593734 521547 586592 306938 795147 188160 764040 077254 428939 534483 147547 035696 057976 300193 995503 004720 224778 347943 788400 251844 692873 418830 407883 645585 354157 190243 912266 398177 870837 837798 216628 773211 286329 394011 557807 316009 236564 823112 514196 564609 319600 200140 595228 125236 033028 391944 012176 801499 619249 845321 823978 013180 833773 503726 861612 495788 918361 087211 002922 902899 332936 108126 178872 332603 258026 187645 885527 731281 448888 268802 715810 145605 897325 399823 090638 795594 659747 022437 973084 060253 369464 824123 050496 688159 239989 598787 053762 990911 833682 576092 920622 182332 627165 896368 553631 103269 849001 193003 694238 454189 795896 306401 665878 776349 162441 183049 613068 264022 146379 352071 717071 903460 384532 366791 736394 329646 313523 880817 786951 915994 373598 503211 367792 745974 227181 288224 179433 147536 989151 405623 437888 685009 734163 798999 405716 516665 033982 604925 839794 635496 541048 132638 116291 224690 318580 914917 296775 128134 908428 947393 368551 033873 463412 153766 547429 162491 508437 813958 856463 270290 373691 902075 172728 314224 275089 317954 245175 047441 422393 052064 385084 827935 342847 145089 681738 127412 817791 016363 641391 225444 213136 741123 700739 758343 478416 143082 633957 642155 493204 770669 558166 423754 093268 389114 951327 439665 706733 591094 498456 440224 579473 761669 841013 391304 425277 949188 786781 832358 426901 308218 152100 980102 222648 265713 650810 545184 340775 437164 493090 390020 130329 068373 183783 681505 612017 472238 984735 052517 399513 176576 756822 430920 924594 221574 989928 112267 980530 376932 203421 334913 286382 505392 454827 960271 086419 359806 850138 481106 694308 665931 781802 834553 814487 635231 793401 013922 287342 729424 940968 011734 760827 558914 454082 940176 939793 731522 146756 925820 272929 325357 969943 119799 410319 666055 969994 524450 515654 570806 157748 610768 044663 621415 335634 756945 828073 506975 580999 054565 561975 866579 148363 065572 685649 893963 798783 950010 402859 937910 796056 009845 133197 503016 902483 521517 554992 544730 935313 610656 575700 576438 204564 132742 791853 225340 006076 576671 254788 468534 109211 164734 395592 875946 731592 121536 173808 502295 417668 728110 521035 956526 132967 / 527 > 811065 [i]
- extracting embedded OOA [i] would yield OA(811065, 1067, S81, 1053), but
- m-reduction [i] would yield (12, 1065, 1067)-net in base 81, but
Mode: Bound (linear).
Optimality
Show details for fixed t and s.
Other Results with Identical Parameters
None.
Depending Results
None.