Best Known (84, s)-Sequences in Base 7
(84, 64)-Sequence over F7 — Constructive and digital
Digital (84, 64)-sequence over F7, using
- Niederreiter–Xing sequence construction III based on function field F2/F7 with g(F2) = 21, N(F2) ≥ 2, and N(F2) + N2(F2) ≥ 65 from GarcÃa–Stichtenoth tower as constant field extension [i]
(84, 104)-Sequence over F7 — Digital
Digital (84, 104)-sequence over F7, using
- t-expansion [i] based on digital (43, 104)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 43 and N(F) ≥ 105, using
(84, 526)-Sequence in Base 7 — Upper bound on s
There is no (84, 527)-sequence in base 7, because
- net from sequence [i] would yield (84, m, 528)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (84, 1580, 528)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(71580, 528, S7, 3, 1496), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 070089 710884 629111 253867 817780 648121 205349 954665 595986 466709 464850 990329 115088 037192 018051 437338 569397 549840 278582 535395 208604 813769 008978 552891 041060 101928 453953 528032 560960 404925 398011 617548 922024 073768 487467 139245 632984 641947 872582 931017 418086 316115 322983 811385 397397 299047 994817 570675 593253 047290 628257 758099 743416 505807 823706 782267 618632 774584 534450 881093 023400 834198 731196 279933 860498 818655 321117 421262 384647 684615 831694 326568 999514 442206 478810 031802 227649 279224 448764 463637 884588 663459 535738 949154 433323 392015 789420 616004 112311 521480 264202 061429 760769 593815 438110 955824 581571 830698 042026 219527 953601 327579 866738 586638 315278 421741 479296 821324 458862 773366 917909 380226 677949 260306 306025 388286 062853 841118 535602 692263 387201 646026 968235 648850 422851 376807 473887 126905 122474 623161 377867 798482 705010 609390 780931 991543 740693 000025 005713 819628 858725 756799 910959 861992 245526 879094 100906 108258 774177 669848 113027 552118 553270 910677 767169 337269 965174 321665 175096 508830 998458 033662 080509 973812 301027 888927 678608 669426 126717 278359 816606 152660 326340 168203 948808 581755 897058 598506 088192 305704 187872 259922 084985 824449 625474 951188 494359 339582 043577 659729 244555 943921 478014 368544 092401 217167 850449 452716 376180 208193 098378 911309 768167 894158 068871 438579 129585 257519 855682 532506 704061 566293 179885 104151 522554 671221 657971 649480 363642 068967 172237 107332 060595 / 499 > 71580 [i]
- extracting embedded OOA [i] would yield OOA(71580, 528, S7, 3, 1496), but
- m-reduction [i] would yield (84, 1580, 528)-net in base 7, but