Best Known (87, s)-Sequences in Base 9
(87, 221)-Sequence over F9 — Constructive and digital
Digital (87, 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
(87, 244)-Sequence over F9 — Digital
Digital (87, 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
(87, 722)-Sequence in Base 9 — Upper bound on s
There is no (87, 723)-sequence in base 9, because
- net from sequence [i] would yield (87, m, 724)-net in base 9 for arbitrarily large m, but
- m-reduction [i] would yield (87, 2168, 724)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(92168, 724, S9, 3, 2081), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 25 798965 178050 733290 041695 481502 151232 706510 016621 102075 591329 227729 591463 525900 692030 549684 030572 377655 822260 035902 566776 995235 608166 404687 338065 716196 863825 434200 377644 798606 377217 647216 939694 569559 264261 191553 867113 883332 623552 840229 973787 256862 487365 247883 295270 704092 252366 373495 332264 320507 385004 453524 074820 795590 047908 927575 673547 571981 894274 891236 712959 387214 263939 470046 835988 164420 950720 274078 888505 117510 393058 995954 139592 543073 726482 037224 957704 807011 680049 366502 691697 807307 376394 560900 678725 704080 525512 456136 962097 043908 175382 480091 565272 075490 483995 698626 484815 232787 810336 266828 195134 666853 849965 312438 258033 579629 875801 225056 343637 061816 390130 226737 085715 998406 546388 500942 847642 135273 966445 888257 354503 992422 887146 300708 668530 372315 884012 224411 817439 594574 824847 752772 481236 104076 279115 378340 615262 061666 578071 378922 253675 361517 758856 674202 646174 057244 267611 241102 658688 090704 772224 549723 555231 013250 082609 563727 461621 773766 622467 675416 910947 858041 335212 737129 906511 189676 266471 665270 114028 676523 048580 099968 459830 723384 664410 122594 558251 953322 823060 946743 568853 507184 931338 328117 599696 352484 964043 147780 603379 555223 851478 246365 685899 938221 730584 499244 975785 697838 452309 164637 919800 084266 743122 522768 475524 718792 426027 473355 646215 724215 152409 042497 994967 263470 342303 190407 875159 618122 186484 591163 188933 601622 393904 057998 758732 545841 626292 068081 924418 274609 630190 634782 279824 099018 461279 673811 656281 359340 739696 660819 110803 121656 380819 889336 005723 077341 456818 975284 565990 739506 562363 787920 299288 977686 017314 735940 493605 680177 243932 455846 041699 088903 433473 010999 479261 066003 650341 531538 096378 595245 372960 598637 901812 455130 087873 072260 422885 004771 611576 980057 003287 264895 745760 808477 603242 734119 349133 238003 963474 897723 309757 517235 191559 006307 047561 596285 796972 299098 788772 602219 144680 722871 693093 418980 361926 931433 730457 572456 412589 842365 016912 899230 293492 124531 757248 521265 971436 499414 459875 450006 705753 253916 686526 934904 648373 447172 116890 061451 175054 761367 422643 726028 030930 568818 240730 272125 670246 844617 407737 938066 514331 438324 287863 892821 056365 664731 / 347 > 92168 [i]
- extracting embedded OOA [i] would yield OOA(92168, 724, S9, 3, 2081), but
- m-reduction [i] would yield (87, 2168, 724)-net in base 9, but