Best Known (113, 113+∞, s)-Nets in Base 8
(113, 113+∞, 194)-Net over F8 — Constructive and digital
Digital (113, m, 194)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (113, 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
(113, 113+∞, 195)-Net over F8 — Digital
Digital (113, m, 195)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (113, 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
(113, 113+∞, 817)-Net in Base 8 — Upper bound on s
There is no (113, m, 818)-net in base 8 for arbitrarily large m, because
- m-reduction [i] would yield (113, 2450, 818)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(82450, 818, S8, 3, 2337), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 6 843621 046987 003105 399967 471117 934520 728071 101199 941633 065687 316054 729406 608711 245432 073970 596845 729540 570305 444524 390039 688798 260528 683493 769939 396177 623002 168130 168218 311989 779238 479166 105023 558310 252924 818430 039763 521622 298030 635204 374374 383509 925493 064146 766078 330124 970040 326185 882885 465986 927943 385305 923458 889489 579728 014665 854086 760545 234848 095528 654235 705755 356367 650946 195805 979445 885531 904828 463245 964495 763615 669873 009001 599583 837048 749014 987929 412422 357933 710270 327549 226390 930945 908103 020487 826367 389158 538843 303090 231911 559613 232498 747955 061801 379383 422292 905344 017440 030929 084172 702419 342101 436570 548299 929675 302284 651308 807719 819551 527862 446249 117380 691464 960546 358972 557116 602381 002287 022277 331163 681754 770652 693216 882538 934989 436920 842102 647662 079587 923078 409977 035998 754462 036669 074941 120659 888533 413873 641574 388641 796466 466948 415696 430717 075337 235403 031342 462319 865379 002790 935778 628496 058389 159642 500012 194129 043691 413436 190115 027006 025068 018524 238872 761560 546832 106167 200367 456033 152252 078092 139166 148174 020753 482139 958270 524392 100387 383082 944846 936733 239207 502835 242753 403614 110989 422202 082948 629714 456415 422870 964536 892979 414299 401382 872628 652946 116845 109324 462969 744332 511493 993794 017156 944845 098050 895119 973864 875154 416678 495229 763235 068668 256999 816842 844170 864839 844341 924572 484967 695929 627906 924254 454992 752406 339533 045045 287690 553191 115893 852531 501542 055062 437088 939212 387549 111397 821998 789795 540009 926043 131301 556702 373627 995863 544580 200147 800146 660647 262259 759205 635776 962114 824087 582585 053878 923698 788740 121956 781858 433618 926645 287326 778256 989835 375908 308129 814766 627780 635178 091378 090310 134492 906797 693504 608740 899627 850904 647166 678308 321770 723689 466742 917854 844689 963286 993958 424880 588302 766100 455597 690276 846502 461755 729661 954178 861001 532178 848399 894868 148557 703414 455495 337520 513713 994329 556731 005487 038857 614397 886689 165534 599984 032619 212276 954726 389238 368117 314524 901034 563130 417130 457908 603655 267825 179999 294637 678579 549472 641815 721243 168179 020157 560813 299023 229007 823678 765161 935361 138548 891894 143065 974182 060893 844972 072655 968970 010267 467686 238906 946852 997051 804539 218869 903478 486756 160878 877997 937256 070777 557951 294442 878243 942460 454275 910244 652823 862996 665841 927969 570816 / 167 > 82450 [i]
- extracting embedded OOA [i] would yield OOA(82450, 818, S8, 3, 2337), but