Best Known (186, s)-Sequences in Base 3
(186, 108)-Sequence over F3 — Constructive and digital
Digital (186, 108)-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) ≥ 109 from GarcÃa–Stichtenoth tower as constant field extension [i]
(186, 162)-Sequence over F3 — Digital
Digital (186, 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
(186, 385)-Sequence in Base 3 — Upper bound on s
There is no (186, 386)-sequence in base 3, because
- net from sequence [i] would yield (186, m, 387)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (186, 2315, 387)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(32315, 387, S3, 6, 2129), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 308 991964 460610 028269 332696 119511 976257 455751 781056 643162 642001 656578 089796 384758 984608 469663 030807 186795 914799 442254 900180 540071 976721 679391 646548 932076 587241 659846 932779 933455 394267 797765 478612 748155 931189 337177 190644 545074 772422 533944 592624 568854 135298 501742 889573 721924 718817 206797 330811 678281 562752 741679 522451 186485 876480 166197 385409 559397 171847 608953 105125 252075 123631 692104 548488 915697 145398 484357 447510 507310 864064 063204 379232 593540 289065 647943 551875 794197 620022 800296 946892 330729 045076 106059 371347 999184 674958 934259 214628 366344 690436 754204 879615 389246 514704 001918 251771 409501 339563 911355 933333 600295 160564 558718 787355 801435 421926 142668 490092 675006 835428 688720 537291 862082 791094 281293 202605 169365 520064 698704 204341 209471 422318 457827 937264 129797 840965 240421 445173 209626 556463 931550 714276 284002 133098 702845 211424 616771 420332 648481 658087 344087 657171 986686 775455 110908 520459 189910 530127 913886 899435 149634 040198 194507 607767 159597 431507 142766 441766 137528 579155 901679 493883 028856 723155 045641 914750 285219 817353 149712 625386 754117 634864 040444 222121 171189 942331 151250 852063 706271 025913 866117 401417 597451 181630 / 71 > 32315 [i]
- extracting embedded OOA [i] would yield OOA(32315, 387, S3, 6, 2129), but
- m-reduction [i] would yield (186, 2315, 387)-net in base 3, but