Best Known (84, 84+∞, s)-Nets in Base 5
(84, 84+∞, 82)-Net over F5 — Constructive and digital
Digital (84, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (84, 81)-sequence over F5, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
(84, 84+∞, 150)-Net over F5 — Digital
Digital (84, m, 150)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (84, 149)-sequence over F5, using
- t-expansion [i] based on digital (76, 149)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 76 and N(F) ≥ 150, using
- t-expansion [i] based on digital (76, 149)-sequence over F5, using
(84, 84+∞, 354)-Net in Base 5 — Upper bound on s
There is no (84, m, 355)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (84, 1415, 355)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51415, 355, S5, 4, 1331), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 52 390162 449137 189565 814412 568820 484921 514855 893062 057443 049947 314586 776314 415844 419251 689814 092988 172236 533221 381836 412408 324145 789140 636706 337762 635030 807274 323637 616954 130712 730899 722551 039357 907963 126835 341382 935235 403660 824008 879096 085908 546587 350352 411084 788593 505672 036602 711781 749246 743935 552493 134769 811681 659106 974338 339280 126717 472194 944373 734235 559007 041758 359968 169736 191947 981082 698194 485949 339864 386326 890302 481019 923795 578093 079904 049721 112732 677386 112107 445299 911588 826391 354317 530397 871542 978853 823518 306222 896298 882985 099859 959671 966699 363531 454690 898581 095001 957641 984570 403292 578168 638082 997493 984396 764237 795091 182270 226186 184272 937427 473368 130890 726813 139994 184733 177293 541460 087536 775802 674166 807676 159822 466764 984758 056304 866887 045110 069808 149960 915615 615712 004693 374130 159639 563124 664519 305404 027386 108141 479100 082513 787489 199841 935561 957873 593697 731102 339726 626674 839444 353363 476025 974571 652025 637759 899855 909495 373651 948448 533166 580176 612114 883027 970790 863037 109375 / 333 > 51415 [i]
- extracting embedded OOA [i] would yield OOA(51415, 355, S5, 4, 1331), but