Best Known (92, ∞, s)-Nets in Base 9
(92, ∞, 222)-Net over F9 — Constructive and digital
Digital (92, m, 222)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (92, 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
(92, ∞, 245)-Net over F9 — Digital
Digital (92, m, 245)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (92, 244)-sequence over F9, using
- t-expansion [i] based on digital (81, 244)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 81 and N(F) ≥ 245, using
- t-expansion [i] based on digital (81, 244)-sequence over F9, using
(92, ∞, 763)-Net in Base 9 — Upper bound on s
There is no (92, m, 764)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (92, 2288, 764)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(92288, 764, S9, 3, 2196), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 490 745568 574823 904378 477303 493355 608769 110346 257722 690764 454240 467284 757090 015919 568584 839917 446905 565072 783072 067005 127745 971251 565828 314359 488278 379025 640412 669883 297901 586795 016392 417866 303203 731129 559807 621111 969649 862400 583592 478398 473022 589491 010394 285327 216194 363377 395596 282919 352446 573380 804548 742509 845613 544250 113472 879265 829297 198466 549887 911137 633947 582020 091224 944987 910924 677288 977921 514662 509377 952102 525487 040961 314582 752275 758630 887445 063192 127277 585423 049991 887319 768343 898785 171103 819487 191806 234267 055425 820268 036214 835304 530875 260344 688862 638686 883315 432637 565897 485196 478858 115502 027715 659111 975956 911838 810931 795551 253297 668457 939479 154088 228468 925647 283975 661223 647464 097269 373673 681097 555704 385564 014388 520370 859600 885289 701223 000520 759971 749888 610115 205186 325429 612336 923912 764234 001250 191243 437189 457731 484026 204236 553767 507416 916514 368679 831458 486694 187373 303205 085588 635492 955921 612360 818783 924154 817655 459869 038361 709991 536491 702409 005125 691166 583535 078786 932099 225904 049777 071111 120003 151484 912198 538180 230932 069824 291965 670671 090200 333315 663045 128758 560461 585729 741649 294143 044257 728602 895545 980729 847090 163825 517588 823992 132914 143965 117726 394527 303543 137292 825108 904830 827004 704225 351166 381153 951093 558508 270589 241820 427864 817386 379471 612991 560717 336325 016249 661448 090431 435960 708460 183997 727330 150604 515796 002910 460231 362953 614170 606597 447596 521133 593476 976345 394609 311735 886184 988191 870498 958677 653560 736047 926741 005304 487265 477920 287710 305488 084667 568286 699621 519178 002197 197879 061128 085559 895220 394714 815262 239529 346590 994631 110127 800688 777688 353186 646877 701501 103542 836358 094053 630157 696143 760353 952374 913305 845451 983566 809082 202773 132935 612129 004047 886492 873314 611656 984052 953278 436494 557881 496569 168399 196368 357324 007523 506073 751125 571566 927716 958009 094628 102348 964265 619679 420502 453471 456985 573201 270832 844989 623229 397145 227574 488035 599065 596414 104375 573098 995022 015373 448669 873377 680000 927445 972564 535248 032838 309557 046975 402235 955741 988054 032146 579734 950806 739618 122731 553584 213648 095858 783079 468523 759685 971797 341840 446228 526649 229914 398898 792172 084877 535918 816153 645040 037026 342800 908799 869072 926169 315342 767733 784006 005394 886462 938950 762741 / 2197 > 92288 [i]
- extracting embedded OOA [i] would yield OOA(92288, 764, S9, 3, 2196), but