Best Known (80, 80+∞, s)-Nets in Base 9
(80, 80+∞, 222)-Net over F9 — Constructive and digital
Digital (80, m, 222)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (80, 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
- t-expansion [i] based on digital (79, 221)-sequence over F9, using
(80, 80+∞, 228)-Net over F9 — Digital
Digital (80, m, 228)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (80, 227)-sequence over F9, using
- t-expansion [i] based on digital (79, 227)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 79 and N(F) ≥ 228, using
- t-expansion [i] based on digital (79, 227)-sequence over F9, using
(80, 80+∞, 667)-Net in Base 9 — Upper bound on s
There is no (80, m, 668)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (80, 2000, 668)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(92000, 668, S9, 3, 1920), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 7726 231344 961629 128352 211042 906880 318224 791170 287277 716237 143292 713972 139712 851175 747919 676626 005549 158186 812549 584561 118038 312762 614524 890288 307185 019697 090401 717781 526334 801232 771286 152623 005072 123067 555454 504290 095316 120850 132667 025296 155784 754805 611007 295493 111111 312998 930566 188168 348207 873959 705350 698648 797141 425170 625272 879101 285683 948411 836741 192582 625511 758303 463883 874761 464501 485205 036939 276992 333595 465680 232222 301875 386405 572261 599909 516678 479606 932989 474663 516445 010250 258152 032164 643996 384283 507593 484103 689553 166627 725017 957352 183874 181564 317727 271131 608764 260679 822367 478533 569128 942239 222784 920937 012446 230410 700388 663829 217170 067411 162150 874906 226867 399735 660660 563669 388058 638010 281357 481277 424982 813053 974967 566715 033300 331820 970734 361562 132698 785139 669420 931013 676048 396114 369990 427932 868084 673296 794027 395222 240206 579890 997296 365402 799760 152769 373142 817388 342878 330099 871012 493478 467134 587295 061662 444215 050430 648886 740509 547922 585819 266867 184022 210255 241851 839651 938447 712955 602344 766857 175104 395251 018365 348590 482033 432796 499484 854736 104631 361185 501205 486973 058986 596488 939050 545417 081813 443923 965006 306564 498138 234185 562235 784331 491887 026497 252705 036988 883823 260155 621572 583640 055232 048851 477881 961560 259029 933948 166470 101430 381030 482886 996121 566134 345584 099405 703530 488526 952024 504875 624927 246595 964405 928800 799287 986199 849022 837458 775163 252226 094018 122906 657462 296384 659770 919594 067784 160874 594774 868618 307452 339288 514249 146311 963434 474200 974227 160407 360887 654465 597191 305468 603176 523482 771562 051108 657871 958031 506696 228517 389271 990687 728727 016795 381841 409551 904237 350644 104173 147647 113184 831814 936920 594584 893254 723257 449094 665105 611545 056673 344187 697692 245045 959672 391642 415462 811687 397645 169445 209608 141948 031173 528141 904697 228866 660405 591444 197547 708410 019059 805193 275833 327273 961663 966557 630524 825042 943740 050004 841797 658200 935477 777212 539480 506042 851828 903526 601052 505005 522529 / 1921 > 92000 [i]
- extracting embedded OOA [i] would yield OOA(92000, 668, S9, 3, 1920), but