MinT - Best Known (105, ∞, s)-Nets in Base 8

Best Known (105, ∞, s)-Nets in Base 8

(105, ∞, 194)-Net over F₈ — Constructive and digital

Digital (105, m, 194)-net over F₈ for arbitrarily large m, using

net from sequence [i] based on digital (105, 193)-sequence over F₈, using
- t-expansion [i] based on digital (85, 193)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 85 and N(F) ≥ 194, using
    - F₆ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(105, ∞, 195)-Net over F₈ — Digital

Digital (105, m, 195)-net over F₈ for arbitrarily large m, using

net from sequence [i] based on digital (105, 194)-sequence over F₈, using
- t-expansion [i] based on digital (77, 194)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 77 and N(F) ≥ 195, using
    - Drinfeld modules of rank 1 [i]

(105, ∞, 761)-Net in Base 8 — Upper bound on s

There is no (105, m, 762)-net in base 8 for arbitrarily large m, because

m-reduction [i] would yield (105, 2282, 762)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(8²²⁸², 762, S₈, 3, 2177), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 28406 014666 374772 408076 709647 483724 384020 237133 437733 140679 411627 710562 092101 117909 195458 141238 369107 232831 665893 992646 691628 347738 419373 017940 816363 300175 332730 944007 857414 208734 535339 988702 384533 564322 036786 266929 661398 562320 254322 970531 751966 383154 709498 939471 761446 216087 435768 002752 297165 046625 748948 592712 997101 304093 226926 043830 756259 578533 264154 649932 750186 332023 564544 975615 249131 496312 317313 193892 218953 155445 437032 558017 558078 319994 214360 207822 879724 291113 535704 238937 345238 976735 591096 325763 605335 506391 488365 260037 361680 844059 722192 686830 370975 198176 852316 244222 094756 617622 813061 468451 527067 662833 069898 060834 141558 235723 913504 890173 131629 600836 382812 396058 742666 836930 622474 712314 367485 058638 529983 948883 463203 318961 944600 045386 402880 777522 621234 610457 754122 969107 677835 861285 074239 959173 885616 559286 728861 335967 700155 876801 284378 362729 918745 592978 127464 643881 499567 624554 978232 660713 812992 904362 404373 135492 627004 046404 872508 000559 151978 535228 484472 698397 100431 624324 706692 577994 650091 861127 105040 765119 975867 448349 479520 161859 254310 478691 431462 347153 635754 355778 620936 654429 459733 964496 264926 686117 069651 484111 766710 345243 768100 536215 960016 570018 896036 378420 000181 730771 697357 572207 928776 981994 069894 163583 329008 996600 642018 586040 230981 217356 508432 835447 011140 104583 668555 280250 452559 023251 359797 409132 088885 513094 323446 193437 100047 237016 205551 025959 115813 024994 905487 934182 442349 125263 335433 598889 960077 590352 296460 548008 465009 565074 910080 368282 677006 004050 111140 396865 109978 675919 745033 319346 672397 607744 306959 476879 790368 956090 181086 033471 645267 251701 668545 676970 282548 341928 359285 735788 096391 560533 801694 816222 469362 036726 975396 395460 140419 827798 555889 558760 017831 063677 750647 894519 646800 928466 213503 335507 336733 232859 398107 407855 169522 418508 816919 751316 303104 109562 102639 850235 193502 756499 694951 729760 000572 545459 479045 767679 541819 162986 569707 907368 688743 484513 511887 802542 757125 841055 839734 045637 563103 447086 161559 534624 049779 184090 576626 044468 699684 568447 147444 654722 206352 384905 313152 894264 830790 268836 289274 538508 930301 665122 225550 786560 / 33 > 8²²⁸² [i]

Best Known (105, ∞, s)-Nets in Base 8

(105, ∞, 194)-Net over F8 — Constructive and digital

(105, ∞, 195)-Net over F8 — Digital

(105, ∞, 761)-Net in Base 8 — Upper bound on s

(105, ∞, 194)-Net over F₈ — Constructive and digital

(105, ∞, 195)-Net over F₈ — Digital