Best Known (210, s)-Sequences in Base 3
(210, 111)-Sequence over F3 — Constructive and digital
Digital (210, 111)-sequence over F3, using
- t-expansion [i] based on digital (189, 111)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on function field F4/F3 with g(F4) = 79, N(F4) ≥ 2, and N(F4) + N2(F4) ≥ 112 from GarcÃa–Stichtenoth tower as constant field extension [i]
(210, 162)-Sequence over F3 — Digital
Digital (210, 162)-sequence over F3, using
- t-expansion [i] based on digital (151, 162)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 151 and N(F) ≥ 163, using
(210, 433)-Sequence in Base 3 — Upper bound on s
There is no (210, 434)-sequence in base 3, because
- net from sequence [i] would yield (210, m, 435)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (210, 2603, 435)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(32603, 435, S3, 6, 2393), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 129 115651 527447 187824 216824 090466 056147 707011 123653 302490 632780 076496 399859 402253 932153 873989 108036 454085 128397 495055 812294 770554 238344 522216 481964 515774 626300 454344 085471 025730 202670 506437 616201 836375 845135 885416 381108 944518 114740 063992 880771 165712 490284 326842 283004 295483 830138 803447 667961 659752 205189 153153 089089 772382 988633 524053 608666 410600 970770 698589 557686 005559 650708 956819 497689 191207 291440 354801 733711 656018 837941 831998 590564 574004 785644 563481 563001 524163 951866 978819 147488 968081 639950 083346 642174 647962 792420 518229 436267 821632 578218 283532 894328 883404 034327 419549 250218 499951 903237 157576 690894 122718 557077 566559 241499 260689 923537 314401 862132 166571 580135 337263 038663 774856 616797 928738 046108 571825 196439 070541 013624 861871 683140 508094 978248 790656 918014 625960 124375 258209 209292 730895 163609 271687 762862 427327 852172 065755 889681 037177 922966 503608 612144 809568 506260 854342 944176 702635 541373 687288 536378 528524 536181 661201 985030 023550 512393 049650 488807 894316 589556 522014 284024 193395 304744 521709 357451 975120 423791 673293 646014 727871 403841 246537 388977 744193 452502 997416 030589 572999 165931 932182 593226 884111 992219 711729 594020 777675 434394 407071 471719 671463 335479 406051 816295 640172 549126 360936 596927 141693 294048 869109 943623 000554 596649 997013 080744 827942 / 133 > 32603 [i]
- extracting embedded OOA [i] would yield OOA(32603, 435, S3, 6, 2393), but
- m-reduction [i] would yield (210, 2603, 435)-net in base 3, but