Best Known (121, 121+∞, s)-Nets in Base 5
(121, 121+∞, 104)-Net over F5 — Constructive and digital
Digital (121, m, 104)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (121, 103)-sequence over F5, using
- base reduction for sequences [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- base reduction for sequences [i] based on digital (9, 103)-sequence over F25, using
(121, 121+∞, 200)-Net over F5 — Digital
Digital (121, m, 200)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (121, 199)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 121 and N(F) ≥ 200, using
(121, 121+∞, 503)-Net in Base 5 — Upper bound on s
There is no (121, m, 504)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (121, 2011, 504)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(52011, 504, S5, 4, 1890), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 106108 278766 904080 105286 170700 553156 143400 702334 228245 109987 869177 725735 787346 861315 395132 730690 775211 223546 862830 813115 172508 468838 432124 663484 194859 301645 353751 313733 223592 819956 221986 610468 811039 580647 149516 632034 299011 510945 817462 816246 398094 132406 980226 903903 928158 066149 484638 441377 711689 615654 807168 580726 604983 203349 496546 873342 595896 573598 617393 992875 412952 258795 377430 364771 103247 856110 024061 367549 301322 372642 365935 292772 535860 992038 967641 018008 309770 253352 535247 926788 762807 740182 671728 434622 810806 638089 670629 150864 785920 418657 577351 494477 769424 191513 949319 931691 801446 365393 933439 720577 380159 111328 087494 311743 210272 218221 571262 371654 539436 597496 442535 008122 260943 975381 780358 174730 756405 596938 972475 582493 080679 327897 652275 985740 701817 425193 494687 672676 196688 780864 878986 980704 073335 205060 657860 516385 026743 063555 777982 810329 812451 403640 372822 256791 324916 283004 922652 682910 276009 840558 511082 532105 577742 730619 697806 914873 468155 298891 696644 868651 035298 286771 490393 450794 336703 261267 560997 347019 472951 906513 429132 057667 958498 568493 308147 740386 387513 328031 413809 006815 844906 528964 900608 726226 729270 314912 098179 937824 086637 541116 837984 556845 812897 280414 393801 245599 059559 110799 422436 867822 627551 921174 643994 298799 155296 661317 814871 393908 987051 704432 287068 235920 552386 672110 203702 867976 432703 920674 980335 461146 439404 422982 130364 077039 719821 194763 198816 282223 461981 981671 442554 215900 599956 512451 171875 / 1891 > 52011 [i]
- extracting embedded OOA [i] would yield OOA(52011, 504, S5, 4, 1890), but