Best Known (9, ∞, s)-Nets in Base 49
(9, ∞, 59)-Net over F49 — Constructive and digital
Digital (9, m, 59)-net over F49 for arbitrarily large m, using
- net from sequence [i] based on digital (9, 58)-sequence over F49, using
(9, ∞, 92)-Net over F49 — Digital
Digital (9, m, 92)-net over F49 for arbitrarily large m, using
- net from sequence [i] based on digital (9, 91)-sequence over F49, using
- t-expansion [i] based on digital (3, 91)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 3 and N(F) ≥ 92, using
- t-expansion [i] based on digital (3, 91)-sequence over F49, using
(9, ∞, 500)-Net in Base 49 — Upper bound on s
There is no (9, m, 501)-net in base 49 for arbitrarily large m, because
- m-reduction [i] would yield (9, 499, 501)-net in base 49, but
- extracting embedded OOA [i] would yield OA(49499, 501, S49, 490), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 378582 303962 290149 918310 315621 007626 781483 582589 084788 609844 508273 067655 949119 280756 937229 597866 728395 184775 115067 534843 544118 884139 893250 379699 220979 400378 130166 223713 273243 830867 948228 158287 772898 161745 059362 349072 583746 010293 255495 847755 955245 198742 686975 529434 906584 454794 790085 515156 296439 145422 382520 911365 513580 724121 878491 509657 099612 044415 610049 203330 425721 302458 033878 163477 766866 934461 944616 222130 199985 473001 621205 102612 876706 830971 186830 290055 502535 342022 545089 418453 564683 420676 191852 308091 847422 311613 990150 676393 323156 407123 458734 418005 412453 040499 712294 539924 846462 697837 005810 795499 392710 834723 872848 615222 909432 921055 117403 093960 297397 235114 990294 600527 359692 104144 961021 228108 099537 210675 220780 135612 720560 912900 980294 591656 557151 768938 839957 597689 328146 899719 582203 153095 262053 915045 208675 084413 309122 124782 553285 044086 600011 / 491 > 49499 [i]
- extracting embedded OOA [i] would yield OA(49499, 501, S49, 490), but