Best Known (184, ∞, s)-Nets in Base 4
(184, ∞, 200)-Net over F4 — Constructive and digital
Digital (184, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (184, 199)-sequence over F4, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
(184, ∞, 220)-Net over F4 — Digital
Digital (184, m, 220)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (184, 219)-sequence over F4, using
- t-expansion [i] based on digital (181, 219)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 181 and N(F) ≥ 220, using
- t-expansion [i] based on digital (181, 219)-sequence over F4, using
(184, ∞, 569)-Net in Base 4 — Upper bound on s
There is no (184, m, 570)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (184, 2844, 570)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42844, 570, S4, 5, 2660), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 201706 606997 246183 115097 056934 317072 899807 729717 017185 370904 679229 101837 160997 871046 819711 315307 316155 548263 901911 529726 410030 522382 164179 375003 627999 111632 632389 124796 423173 887877 655631 610427 658568 913180 134642 826872 379364 545504 645901 538334 653550 347793 507303 156333 193487 345378 723839 980685 806997 836751 038034 425199 116198 313071 741744 251807 524309 767624 212708 818547 996150 685971 703904 448007 766588 756098 271390 893968 423133 934587 279510 619103 922522 827999 815313 687541 896608 552481 871289 092507 346572 646804 837322 783371 294257 474211 874376 224801 382412 621820 655266 049266 229751 466877 463626 117141 850596 775783 508242 648588 840766 454483 399971 837805 692898 532040 530939 556663 303151 011652 852219 185790 469266 884526 936472 193334 453870 016184 114778 916172 322645 317981 907052 495567 951492 169566 326795 290158 424111 862801 813737 853837 936411 356471 301619 817053 971381 002584 393850 301937 624893 078036 356057 715621 830705 934891 270068 828235 021129 732084 792691 892681 523079 728580 506278 262090 803608 237783 293272 945368 205389 991082 399902 941754 342558 168836 889445 624708 492780 103277 731107 839215 736244 422504 263987 063339 904293 107398 778824 667789 913500 533881 820956 478477 867821 953712 043567 400030 291827 922977 574497 040028 299188 147268 464295 053997 043847 260286 597426 844944 846732 996813 712285 428408 779875 253129 908845 257492 422539 533882 975276 185375 049285 612211 781949 781870 082525 756419 829728 846704 159242 948702 965746 385347 844548 630608 803492 692041 137214 011778 044913 723021 845081 116502 115320 340399 415203 874834 944583 313856 421641 798743 965050 393020 988078 710394 164012 355681 616293 771161 730011 591381 197346 935225 964347 175916 205462 979861 514561 466933 297873 805462 936248 010260 163553 519398 135211 216836 095250 253706 046891 956987 746671 547271 248261 430079 326959 148301 936921 777442 936534 862716 452148 053486 572794 806272 / 887 > 42844 [i]
- extracting embedded OOA [i] would yield OOA(42844, 570, S4, 5, 2660), but