Best Known (70, s)-Sequences in Base 9
(70, 164)-Sequence over F9 — Constructive and digital
Digital (70, 164)-sequence over F9, using
- t-expansion [i] based on digital (64, 164)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- T4 from the second 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) = 64 and N(F) ≥ 165, using
(70, 191)-Sequence over F9 — Digital
Digital (70, 191)-sequence over F9, using
- t-expansion [i] based on digital (61, 191)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 61 and N(F) ≥ 192, using
(70, 585)-Sequence in Base 9 — Upper bound on s
There is no (70, 586)-sequence in base 9, because
- net from sequence [i] would yield (70, m, 587)-net in base 9 for arbitrarily large m, but
- m-reduction [i] would yield (70, 1757, 587)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(91757, 587, S9, 3, 1687), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 90421 478294 162270 947142 178087 652019 706826 310141 618366 692961 528917 065873 717310 587084 630944 670105 534899 382857 844352 256012 439980 452115 520036 132746 479423 510154 660926 581959 439281 655994 761532 953614 276017 140388 821937 559089 996361 264146 627984 530995 032067 241060 880553 744502 429080 394866 048193 813015 447802 731774 080617 099237 771418 156865 270886 757308 122986 017180 203020 008872 315359 308931 299106 123574 211440 476234 669262 922206 160418 791015 854396 038626 182121 477749 122007 039596 456957 104833 078327 285801 719551 128832 023616 288200 219298 799972 855959 629832 193052 795179 640640 085166 293319 398805 762460 943219 109245 966132 712155 519348 565112 656814 991771 196620 592304 702914 043735 877196 541714 250698 927717 007799 519696 182059 274607 809317 413982 098100 926492 197060 794831 867032 376785 651950 377696 428405 424398 858227 851382 438103 794085 044078 647969 269557 166087 862388 416157 708915 829091 294147 030961 097553 403499 433181 974153 592168 883833 590792 951624 714697 235670 124732 957408 858367 606700 755482 442547 364875 321542 965499 681320 512090 626699 189326 278623 617770 878599 091315 758372 518773 424741 526560 484573 739182 960165 674005 335789 969718 464748 755490 055497 544271 070454 023911 759023 356191 883937 515283 729526 069690 628911 080656 368766 502278 447158 042252 804914 031091 922504 166526 350808 062367 299910 988599 678348 805041 856163 354703 695528 709184 815561 460776 693844 480479 704441 150214 948013 402918 172856 681150 987531 464999 444241 217595 799018 818760 983955 779100 306156 648819 618107 870430 140246 350157 777010 927528 381858 167472 825679 389836 620775 309121 138395 496536 351118 888130 206604 428722 060462 154584 425747 714322 995845 912947 879081 904105 425301 798095 931055 247864 403304 213238 121477 803210 891331 156469 022566 223019 926105 772369 363895 730869 737496 281693 460803 197299 356486 120439 434017 918025 / 211 > 91757 [i]
- extracting embedded OOA [i] would yield OOA(91757, 587, S9, 3, 1687), but
- m-reduction [i] would yield (70, 1757, 587)-net in base 9, but