Best Known (174, 174+∞, s)-Nets in Base 4
(174, 174+∞, 200)-Net over F4 — Constructive and digital
Digital (174, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (174, 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
(174, 174+∞, 215)-Net over F4 — Digital
Digital (174, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (174, 214)-sequence over F4, using
- t-expansion [i] based on digital (148, 214)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 148 and N(F) ≥ 215, using
- t-expansion [i] based on digital (148, 214)-sequence over F4, using
(174, 174+∞, 539)-Net in Base 4 — Upper bound on s
There is no (174, m, 540)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (174, 2694, 540)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42694, 540, S4, 5, 2520), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 300620 834119 431254 431509 258629 726540 649441 376856 270787 718869 812036 679950 261223 083544 281390 554412 813034 586339 931206 951546 460613 327859 994632 277727 201443 740223 659918 776027 173191 103344 003834 003720 110954 487734 642268 855254 749518 957959 883622 129677 549113 274750 163242 783008 763940 017267 790180 509440 810491 548497 825645 423834 460071 920435 498287 381605 706822 820686 262416 487455 568429 809465 343207 914890 557156 725947 939064 537324 276878 288423 134494 509780 160223 944537 511044 258414 969364 405916 121743 032853 942272 850857 660743 625868 208223 622480 659071 631406 734606 667633 769404 437878 324584 635429 264024 339836 957525 275571 523680 866069 207941 463436 730527 056380 325667 882700 467819 024651 879767 992511 713715 047218 251226 889704 270579 591687 056174 434864 048255 927820 576081 348055 733109 795703 105254 940303 094008 576661 429086 438381 840121 355253 228069 784749 688313 146203 818456 132963 978661 060855 557256 217054 691998 981729 733887 546725 851828 566496 866685 545058 692807 376398 940642 588766 962665 730710 488440 796749 398262 452388 207397 922008 921582 820024 961828 381320 114271 805294 109627 537735 291191 089404 807670 730825 991317 071879 343654 562956 928952 950941 301621 303720 729836 389794 549998 334021 737629 397205 368002 158361 092992 726674 393777 564955 493085 680801 847966 078860 189486 714868 625253 482882 806224 149215 218521 462107 069059 796632 042352 430613 896333 612122 019127 586483 172449 550953 282594 933354 962905 359683 597561 827833 294888 477875 316823 511063 565410 356057 322463 704701 363535 660453 870571 287855 034732 369559 560457 836866 088176 467610 289905 352483 325903 235429 176628 130133 368525 891594 132587 492766 412938 281548 731970 240015 613817 304920 305608 426006 952366 810527 642296 322875 488158 389789 422762 690388 673761 629897 895290 777481 773056 / 2521 > 42694 [i]
- extracting embedded OOA [i] would yield OOA(42694, 540, S4, 5, 2520), but