Best Known (92, ∞, s)-Nets in Base 8
(92, ∞, 194)-Net over F8 — Constructive and digital
Digital (92, m, 194)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (92, 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
(92, ∞, 195)-Net over F8 — Digital
Digital (92, m, 195)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (92, 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
(92, ∞, 669)-Net in Base 8 — Upper bound on s
There is no (92, m, 670)-net in base 8 for arbitrarily large m, because
- m-reduction [i] would yield (92, 2006, 670)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(82006, 670, S8, 3, 1914), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 171 394804 365506 750795 164719 274078 325897 414411 042353 966957 807593 846592 289012 769063 950792 501031 408936 135173 888020 808701 018118 829254 031007 719316 143502 924944 997188 106087 686595 416324 179456 211451 604380 585085 389454 639596 294769 042616 497585 209916 018790 013459 041115 729841 591489 404043 641554 639072 109325 263254 283455 574210 308433 489597 591239 328785 595695 140905 256961 540988 877094 671407 835286 593839 631485 644037 430726 591413 470068 162383 985638 426887 073419 503228 615803 960395 479232 090188 173468 340311 791632 292860 110229 540621 090806 921285 533111 286904 673081 040010 405363 220055 640394 180743 201394 697540 462763 812287 250175 500146 929631 937452 105985 847685 917508 941665 195834 545626 013997 545607 793515 734770 045163 518298 287449 959927 175703 723657 314825 659390 569729 074459 649521 086537 372446 699983 819522 895253 073030 819164 745872 093077 796913 453800 137517 383587 143023 558898 434956 100067 030027 503021 732924 748157 479350 897275 607218 189169 562908 403687 646722 533005 222587 564471 856772 482556 578357 799718 248497 858483 965173 376717 034828 624040 532577 928726 453121 138234 858318 659652 137386 343343 605345 679706 021774 364773 706583 840490 342936 175452 750837 720764 947845 136131 998509 324448 456904 300443 954477 469578 999734 310096 653200 735463 765119 801153 359275 312919 008493 443058 744921 289664 263877 780930 197394 846787 332296 916928 702505 480168 898501 015167 634818 665574 836820 586012 073451 976065 302759 602751 853373 577132 428965 099368 849896 670566 984332 164631 222365 440904 700382 458527 645929 398421 299430 754155 343002 509133 382815 380080 461741 539350 156210 667081 318233 315747 045532 576939 698167 392686 727022 810089 397823 305103 799435 488061 696337 921701 119999 281478 882808 109292 232031 164418 616572 528580 734761 311405 442640 790685 400050 357385 106752 059042 235179 303307 981601 227564 862793 683922 093042 896549 578600 451979 964681 030701 856294 556884 758099 988469 386837 043229 619439 832656 178781 833081 026389 003692 396774 808847 751441 172511 326208 / 383 > 82006 [i]
- extracting embedded OOA [i] would yield OOA(82006, 670, S8, 3, 1914), but