Best Known (91, ∞, s)-Nets in Base 9
(91, ∞, 222)-Net over F9 — Constructive and digital
Digital (91, m, 222)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (91, 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
(91, ∞, 245)-Net over F9 — Digital
Digital (91, m, 245)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (91, 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
(91, ∞, 755)-Net in Base 9 — Upper bound on s
There is no (91, m, 756)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (91, 2264, 756)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(92264, 756, S9, 3, 2173), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3087 575943 864038 933944 657494 815858 702103 321298 096075 375534 840127 022301 468366 505210 922024 927423 620129 413042 199721 955136 014956 921295 473017 173853 639276 789600 014028 068784 523492 282553 495627 511705 942327 895507 028938 551856 881844 341573 948529 391719 856290 749994 720867 687291 372182 584918 668413 595415 704627 875001 032010 461161 956881 953665 510759 208622 361185 708997 080829 803032 370870 762747 267058 509142 679388 425153 578485 917490 180817 152223 126827 994996 822529 340987 552464 820574 258680 726053 069325 139394 140659 051133 000590 480561 678907 171708 362266 303242 477625 977110 408260 022527 226054 564942 439864 600387 790484 256234 865512 040699 486301 093559 870159 635611 959757 075665 728762 322113 977042 292551 510843 816019 539207 793844 819429 078214 673923 807882 704349 678737 657225 259279 520975 230528 159134 611532 313186 466250 143447 254372 954156 430937 005414 428811 768821 597861 577664 396289 843898 647986 634169 810825 396496 618020 582689 705842 293587 717489 921192 776179 769775 523817 224074 885330 113814 146067 601220 583358 017742 041146 008504 927256 302425 943200 870280 330526 682490 956568 832218 074193 597640 868536 076564 022937 910264 677022 559459 753575 059541 582084 828342 334121 039239 918835 438750 513782 274998 529756 793345 085398 225074 171622 481605 520757 088346 823418 716010 486604 488198 774859 985700 451198 311301 935454 392658 815113 244508 273678 630524 490901 844069 957362 266753 492663 860899 628037 255758 519275 950518 017293 078101 485913 597860 745548 464236 733599 391313 684752 634680 402120 085327 734251 025766 966997 171997 429577 482874 470854 596512 973550 684851 136124 309248 237193 624600 562460 179755 691468 649118 135862 991881 897988 403573 980113 227318 655186 764474 380075 645176 070697 960198 889575 514985 925614 670571 727158 721278 229291 953105 618645 694803 797173 687961 953016 955922 344146 347606 276140 675508 306122 262393 093431 207212 452404 729334 407256 011453 863083 211605 775012 173237 916677 572571 518109 695421 985051 911892 332247 315427 834421 973269 875072 144040 498358 861275 673320 854440 379586 725997 370714 379515 280470 049198 548239 492619 313461 285393 996674 348812 798784 968891 934861 015660 720822 859312 298439 288905 526383 688322 971170 984761 082359 139678 677655 504576 772213 149424 241059 721519 604552 011884 085748 421621 635357 107226 139435 304223 426372 235068 724835 223346 376488 680757 674227 311119 617810 814639 824558 405253 118634 127615 / 1087 > 92264 [i]
- extracting embedded OOA [i] would yield OOA(92264, 756, S9, 3, 2173), but