Best Known (31, s)-Sequences in Base 9
(31, 77)-Sequence over F9 — Constructive and digital
Digital (31, 77)-sequence over F9, using
- t-expansion [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
(31, 119)-Sequence over F9 — Digital
Digital (31, 119)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 31 and N(F) ≥ 120, using
(31, 272)-Sequence in Base 9 — Upper bound on s
There is no (31, 273)-sequence in base 9, because
- net from sequence [i] would yield (31, m, 274)-net in base 9 for arbitrarily large m, but
- m-reduction [i] would yield (31, 545, 274)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(9545, 274, S9, 2, 514), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 6 958008 525956 789265 608060 783885 932988 171604 150606 352429 336613 480224 424089 117469 263763 573172 826813 523756 645714 304680 259217 812461 688470 641061 606537 344658 995065 489946 620884 531994 925961 597300 635607 806758 458598 747623 678817 654929 180584 387724 120617 070592 978153 307697 740634 596878 099062 237248 092196 065784 514892 262384 133135 358804 423680 007279 758194 905848 731236 794445 914765 900476 799533 723454 234296 955010 751168 184360 114080 596360 980461 302424 263192 094439 514192 651188 810232 983023 496445 520588 731299 298220 021652 035852 613754 817921 932354 333747 / 515 > 9545 [i]
- extracting embedded OOA [i] would yield OOA(9545, 274, S9, 2, 514), but
- m-reduction [i] would yield (31, 545, 274)-net in base 9, but