Best Known (148, ∞, s)-Nets in Base 8
(148, ∞, 194)-Net over F8 — Constructive and digital
Digital (148, m, 194)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (148, 193)-sequence over F8, using
- t-expansion [i] based on digital (85, 193)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 85 and N(F) ≥ 194, using
- t-expansion [i] based on digital (85, 193)-sequence over F8, using
(148, ∞, 259)-Net over F8 — Digital
Digital (148, m, 259)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (148, 258)-sequence over F8, using
- t-expansion [i] based on digital (141, 258)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 141 and N(F) ≥ 259, using
- t-expansion [i] based on digital (141, 258)-sequence over F8, using
(148, ∞, 1064)-Net in Base 8 — Upper bound on s
There is no (148, m, 1065)-net in base 8 for arbitrarily large m, because
- m-reduction [i] would yield (148, 3191, 1065)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(83191, 1065, S8, 3, 3043), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 49850 140112 461698 521776 508680 064179 702378 194423 656010 681102 448319 730327 397809 781551 422201 393828 596250 927704 912592 474263 165536 355815 675986 986872 698304 876401 053555 679798 548617 337203 782366 064372 291912 545315 719811 791781 070978 840572 196198 105124 290344 599829 606053 278535 893224 974332 356564 295812 922545 786299 289328 952717 937222 677712 591967 124081 671843 694235 060902 936967 933538 026548 687406 837254 899794 389880 391558 361443 635130 421708 277554 755571 710240 135700 911346 706348 391498 672840 374529 930220 802353 571758 837510 190286 656984 644261 556705 800564 947680 700394 829085 726771 238207 460826 296065 831128 021738 426542 552962 253057 845168 979177 015499 231550 028833 853110 852844 686137 154906 849247 846028 160182 571808 042953 451495 901982 004076 045459 292817 116584 889100 625627 729106 843933 337772 763988 338089 471316 047917 176577 519629 052714 547988 050688 253887 726753 462085 272767 858759 676086 256263 252434 542625 859850 133600 486808 133925 337517 007713 592178 461250 370059 861013 531485 841621 302819 186067 196740 345496 255162 130181 964707 872510 187493 892202 953690 068741 060291 971341 867950 742477 370708 427535 391079 205874 717537 901512 324732 576113 158961 069659 098823 146021 257316 052443 695705 379068 892079 554940 976172 220889 451490 129856 843933 865612 669855 113900 487113 815222 104351 287571 767177 045502 511898 815280 682563 610249 762549 189832 638430 404639 847593 910855 408171 183199 270156 204034 779373 602920 836417 384300 446018 450954 728131 133511 049367 965672 771933 509930 638218 000212 619229 147673 637295 615372 160422 816365 726673 504490 877495 670581 901792 994448 049478 914192 413414 936783 024747 129097 536995 235556 853784 109790 279716 515430 406838 395609 767993 240177 587546 101184 400715 269886 680555 413249 088404 694602 070518 118021 401612 720010 869828 951082 652122 773396 774859 884556 607770 044020 571220 173613 202291 737897 996587 396840 448457 223356 348724 243516 754779 264558 200274 510702 330562 652223 772945 171180 650722 173877 776683 720576 325676 075964 707656 778328 259758 371359 692252 494981 835844 325098 821179 126363 455110 879437 151651 590289 649019 413633 651766 391280 135620 572525 101900 766858 010606 661168 906717 233257 965625 873200 872539 188191 328685 010514 890149 964591 903481 526687 169190 174338 956867 705743 821327 721104 920921 131426 004056 243785 989649 904360 879547 945576 617951 112866 624593 560781 591666 906338 068644 171219 616191 753890 034599 435212 814099 676240 922229 589879 697349 264425 650551 315647 867082 436850 558498 443537 755655 606657 331036 557970 559119 313867 847780 016019 160677 129075 478830 620056 898483 156083 357546 810550 190675 393096 086927 953663 139813 006520 288291 887871 891054 854811 467451 310863 326354 508117 917495 968535 388341 132143 128946 649523 698815 238857 198982 720943 214403 687422 302759 401946 832208 011006 058652 072671 104928 839642 333489 308551 363280 494325 056468 534051 315672 892418 389242 809437 440615 436488 740466 644116 420205 069568 641485 552115 262780 347445 124176 216118 697979 382647 843227 417379 966725 105876 093412 649290 022613 141196 619060 077943 457046 291798 053104 837585 489821 263632 787202 631373 329711 124097 421791 179520 617854 504045 688091 280204 438336 276017 802454 761472 / 761 > 83191 [i]
- extracting embedded OOA [i] would yield OOA(83191, 1065, S8, 3, 3043), but