Best Known (89, s)-Sequences in Base 9
(89, 221)-Sequence over F9 — Constructive and digital
Digital (89, 221)-sequence over F9, using
- t-expansion [i] based on digital (79, 221)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 79 and N(F) ≥ 222, using
- F4 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 79 and N(F) ≥ 222, using
(89, 244)-Sequence over F9 — Digital
Digital (89, 244)-sequence over F9, using
- t-expansion [i] based on digital (81, 244)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 81 and N(F) ≥ 245, using
(89, 738)-Sequence in Base 9 — Upper bound on s
There is no (89, 739)-sequence in base 9, because
- net from sequence [i] would yield (89, m, 740)-net in base 9 for arbitrarily large m, but
- m-reduction [i] would yield (89, 2216, 740)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(92216, 740, S9, 3, 2127), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 61107 194940 675794 361009 216725 424911 191116 580721 803737 270481 071693 837092 189074 737438 206216 750812 596825 498306 920827 845804 213300 164469 103740 421421 214807 398901 358033 186491 068256 058905 456365 162064 675284 317076 327714 731393 582054 669414 998242 193306 202868 302283 566843 910067 577762 531436 256365 932023 945499 686051 275976 177512 820396 330517 443773 850984 556210 717327 046510 124652 916631 563831 509527 081711 601362 104900 160836 186466 509339 083105 946763 291886 052986 378139 865695 246378 257329 840879 005233 529574 242416 865226 405246 457875 628289 076867 190881 106961 449516 617086 052698 444425 058109 157101 694871 871317 811805 350181 518651 985097 709487 447512 716043 607602 824272 584205 121691 758233 196223 026665 388710 807816 567127 759518 315413 022457 041544 173038 146064 377357 682359 326952 110871 111723 978067 469885 623531 309347 466593 425097 655493 334633 977142 549335 246839 119221 937793 953597 761715 530726 666348 089920 842494 627965 737181 065862 043660 973016 199922 679542 595565 307295 923829 433176 046258 508448 043174 281407 475289 807360 768070 691070 459112 473679 616642 374760 236963 831577 266663 550252 656284 961341 558447 784805 250332 000196 343479 969662 493245 729299 604267 747435 317298 526394 362610 291602 321013 793439 882624 005552 575625 615426 747467 626361 624742 284571 950849 086092 166420 807373 433234 033656 941737 770167 880592 894474 699502 691574 302397 887835 934675 258253 882182 436210 101732 421792 249751 524063 282879 668089 367031 488172 819740 427187 405030 437543 083762 768175 914672 960779 538428 988951 019076 565158 555610 339197 435141 822558 279866 330243 010110 531430 652564 468408 558594 248249 962459 342601 745290 742800 265725 953520 325692 016910 185704 156372 511928 727704 000432 820638 043957 816057 169680 358077 256743 500744 590115 934321 057047 686899 079504 188040 305258 902345 919498 457361 447418 981564 769041 625775 007500 678253 708018 996474 313509 148382 398144 537358 233183 513294 118912 262543 393806 119995 814604 744738 865152 481839 989546 043186 901960 050718 946169 844252 498651 361392 828693 345026 573287 887884 743626 561144 161399 138900 323943 785567 428585 993141 174287 074770 714584 950997 791581 343789 501744 512638 471522 010960 467996 133994 159145 090484 216439 618980 312362 754656 904100 632926 187258 307851 600007 971417 074406 740953 627741 113690 854198 730431 748744 810347 067717 581715 795673 / 133 > 92216 [i]
- extracting embedded OOA [i] would yield OOA(92216, 740, S9, 3, 2127), but
- m-reduction [i] would yield (89, 2216, 740)-net in base 9, but