Best Known (123, s)-Sequences in Base 3
(123, 77)-Sequence over F3 — Constructive and digital
Digital (123, 77)-sequence over F3, using
- t-expansion [i] based on digital (121, 77)-sequence over F3, using
- base reduction for sequences [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 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) = 22 and N(F) ≥ 78, using
- base reduction for sequences [i] based on digital (22, 77)-sequence over F9, using
(123, 119)-Sequence over F3 — Digital
Digital (123, 119)-sequence over F3, using
- t-expansion [i] based on digital (113, 119)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 113 and N(F) ≥ 120, using
(123, 258)-Sequence in Base 3 — Upper bound on s
There is no (123, 259)-sequence in base 3, because
- net from sequence [i] would yield (123, m, 260)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (123, 1553, 260)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31553, 260, S3, 6, 1430), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 62014 449464 184201 662420 203631 798028 384565 206042 544991 498559 908026 945444 585077 298290 425453 811353 436619 305645 098464 441919 884519 796788 611159 633766 528910 485164 504923 851868 943463 112831 772552 284920 099892 995569 417923 404645 345994 615753 520578 572969 580153 024367 702498 956368 940805 096713 492071 369972 718704 668783 596368 924945 918750 373049 766012 076675 108281 848449 930663 234680 959149 851417 188834 633588 392154 088643 134606 556362 298539 659713 721442 368956 981391 270919 984878 693235 435774 765175 783134 927160 627692 816171 683603 868090 170409 201163 965637 479406 761722 534035 408124 807760 551200 436718 520675 338889 021909 197533 617833 559343 560849 511957 098296 125354 064734 915130 398284 639555 537530 605061 403608 776053 828888 233754 845645 683913 261846 887397 103462 563084 339558 035399 061802 127453 / 53 > 31553 [i]
- extracting embedded OOA [i] would yield OOA(31553, 260, S3, 6, 1430), but
- m-reduction [i] would yield (123, 1553, 260)-net in base 3, but