Best Known (44, 44+∞, s)-Nets in Base 8
(44, 44+∞, 98)-Net over F8 — Constructive and digital
Digital (44, m, 98)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (44, 97)-sequence over F8, using
- t-expansion [i] based on digital (37, 97)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 37 and N(F) ≥ 98, using
- t-expansion [i] based on digital (37, 97)-sequence over F8, using
(44, 44+∞, 130)-Net over F8 — Digital
Digital (44, m, 130)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (44, 129)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 44 and N(F) ≥ 130, using
(44, 44+∞, 331)-Net in Base 8 — Upper bound on s
There is no (44, m, 332)-net in base 8 for arbitrarily large m, because
- m-reduction [i] would yield (44, 992, 332)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(8992, 332, S8, 3, 948), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 100898 690515 380933 014024 789754 677501 925565 142663 352679 782758 856303 944641 926633 714289 360967 477911 984943 474721 752022 223684 436901 130254 028670 147244 542558 307606 207090 858584 025069 711227 422265 603082 042070 128086 680499 759496 083388 471275 378373 647503 967234 966663 573753 984181 416508 585395 819519 500213 736830 498180 218048 230780 057830 199303 091588 904469 823221 781097 460569 124489 877695 078494 765472 384052 275931 407953 721517 524947 795517 396773 245493 813854 045069 009007 327389 033272 335971 240669 112407 691965 517358 262271 065026 392788 701560 897388 411393 367877 815107 323298 411995 733751 969823 526400 293387 343857 657112 428664 147075 719404 037568 571196 349126 330544 255825 089148 520930 619920 105663 742280 812338 174461 007902 120713 611611 560752 228474 634607 216282 349097 795406 291322 491601 248045 065402 614758 831802 425051 668155 658927 607667 217809 431254 065569 012754 656089 681507 588550 395834 159659 233658 460151 314527 958909 340736 743040 148144 295699 455867 355136 / 949 > 8992 [i]
- extracting embedded OOA [i] would yield OOA(8992, 332, S8, 3, 948), but