Best Known (102, 102+∞, s)-Nets in Base 8
(102, 102+∞, 194)-Net over F8 — Constructive and digital
Digital (102, m, 194)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (102, 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
(102, 102+∞, 195)-Net over F8 — Digital
Digital (102, m, 195)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (102, 194)-sequence over F8, using
- t-expansion [i] based on digital (77, 194)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 77 and N(F) ≥ 195, using
- t-expansion [i] based on digital (77, 194)-sequence over F8, using
(102, 102+∞, 740)-Net in Base 8 — Upper bound on s
There is no (102, m, 741)-net in base 8 for arbitrarily large m, because
- m-reduction [i] would yield (102, 2219, 741)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(82219, 741, S8, 3, 2117), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 401 850122 669501 719881 852960 374387 609919 307967 736532 321405 148089 476166 756989 032638 717935 772687 041953 774975 158442 522727 051513 766001 335490 253818 756549 458175 873366 583333 700901 677956 548709 424403 697771 340021 266274 080438 722020 567917 297614 204099 256755 691356 181708 934596 319455 650506 942976 561065 051529 380429 165962 593694 296685 118662 704244 901916 828307 932453 321555 440910 869005 054434 435046 417340 714376 157162 882979 899099 961620 878533 652133 965393 792458 185667 672765 484861 724451 565315 030484 844258 024642 012954 301072 434829 652385 799802 620529 512434 382708 693636 792944 792183 191300 720674 851943 269037 630448 873844 047222 665610 466895 937328 028923 218839 609523 076693 459604 600520 332459 198091 175561 496749 626545 282370 874094 700706 529207 640417 244869 630721 322511 121529 807037 804315 680137 967974 741104 819437 822914 090598 089751 302337 440040 486079 726525 378320 619962 305649 319754 649384 020641 158643 168493 619206 872122 967811 413274 307317 335015 718315 512775 023655 557526 894315 294219 635977 968155 537759 165054 082059 606626 233525 100393 030084 820251 184123 923611 482275 233622 546795 799871 704359 732874 344714 870404 430661 476298 047755 772563 638526 570090 865672 835371 767872 690635 170185 906109 250099 154545 919438 981267 495509 565674 287767 756700 127605 078634 239057 654844 184234 269651 140800 886521 023100 413607 769902 060156 108017 876379 318017 528774 598353 350593 800730 175039 594770 730660 943086 285212 246905 285429 609727 696446 716369 981820 030082 867607 654934 929919 062028 065746 094867 842624 015873 927467 567470 638338 699959 342679 623218 313563 127458 792147 329033 206468 713118 542357 278936 222993 628651 534484 882886 680982 973860 068373 935258 102748 467905 950974 921357 291545 054112 978058 594169 372212 661206 693854 308956 790229 610097 994015 195787 296968 156333 373541 090007 110160 270902 320371 956503 270727 397336 547166 067388 365634 469961 864351 262856 339080 368990 273853 914296 212996 878625 053045 476065 858812 483392 921586 265958 766200 827961 470592 185373 938486 383262 275607 982700 432012 232637 461638 240902 810911 387213 188383 438598 320510 646013 950825 131977 932833 046592 601841 931485 192337 358939 807436 288129 043848 530157 371404 132170 805897 529464 455168 / 353 > 82219 [i]
- extracting embedded OOA [i] would yield OOA(82219, 741, S8, 3, 2117), but