Best Known (192, ∞, s)-Nets in Base 4
(192, ∞, 200)-Net over F4 — Constructive and digital
Digital (192, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (192, 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
(192, ∞, 258)-Net over F4 — Digital
Digital (192, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (192, 257)-sequence over F4, using
- t-expansion [i] based on digital (191, 257)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 191 and N(F) ≥ 258, using
- t-expansion [i] based on digital (191, 257)-sequence over F4, using
(192, ∞, 593)-Net in Base 4 — Upper bound on s
There is no (192, m, 594)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (192, 2964, 594)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42964, 594, S4, 5, 2772), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 17947 432270 765760 845146 195738 797545 646752 067513 252844 617734 862612 163501 113850 122664 952626 995121 129019 834592 462396 565419 484817 315466 560286 589043 370008 700910 715120 372980 947355 898929 749996 303186 872399 923071 248731 483977 570421 435784 899193 073877 197945 423497 624748 608942 381064 174085 518234 618957 642487 497924 694118 231952 032127 433468 857068 015502 912922 344078 590865 185936 316786 705672 837275 492428 857037 953144 443174 388247 372252 192337 184291 124651 137886 819691 101042 925888 447689 996627 922231 277894 356944 539017 550619 410795 860099 889315 764924 496564 504679 733211 957285 166666 153558 156666 392072 468977 555276 633049 654638 114177 302461 165483 102828 725397 588597 133655 939341 374206 944270 735481 262896 314059 822173 658209 944668 177257 380201 118799 936817 412256 082762 206600 243749 403314 584845 187974 735441 932026 882368 648601 413548 722561 116054 831689 291478 045562 376860 990908 295598 890382 683557 354438 678624 250767 215845 920580 940119 333624 216681 823574 826413 144555 370172 253502 583668 477917 339701 953759 032426 704341 973295 690908 285274 652375 934125 149003 800273 281007 009980 013308 657957 148008 037611 945161 182385 064377 613069 167915 131888 250063 694916 157241 364243 679427 560764 487777 987463 642468 684568 664695 546579 642805 863398 864529 967055 698040 559175 777570 582691 191929 599703 525295 290964 239520 315774 530333 998976 543133 510527 607582 654408 184120 815668 481350 768272 921210 365643 982303 133467 674543 588679 840957 769611 148276 991693 614351 176161 857911 820731 261248 531780 738940 453793 446413 858153 005549 382288 717859 998945 537349 312862 954183 489255 302025 345527 690965 777836 464298 064247 595815 292346 127441 193469 340110 015301 147443 544960 645301 933932 496401 389694 621383 521529 095601 471928 650761 826772 500976 121228 730566 244276 917480 578543 192304 386693 618730 804658 338561 417946 258682 990176 426778 729292 305135 842997 508342 296753 365647 991187 369947 798686 380076 714194 942992 122640 097365 583028 289536 / 47 > 42964 [i]
- extracting embedded OOA [i] would yield OOA(42964, 594, S4, 5, 2772), but