Best Known (179, ∞, s)-Nets in Base 4
(179, ∞, 200)-Net over F4 — Constructive and digital
Digital (179, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (179, 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
(179, ∞, 215)-Net over F4 — Digital
Digital (179, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (179, 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
(179, ∞, 554)-Net in Base 4 — Upper bound on s
There is no (179, m, 555)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (179, 2769, 555)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42769, 555, S4, 5, 2590), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 426 518564 910207 537694 209586 479835 195896 115652 838197 555784 120032 641627 445238 326285 474273 566570 872415 361480 682412 234114 288964 942791 632507 991175 423325 704635 811597 285790 595450 496193 424614 228922 956301 048839 434330 775507 677061 656977 215484 557167 312652 360757 902942 254204 168654 765960 425426 347139 676516 554139 484525 656959 293165 134945 786355 136985 080340 783095 367846 354641 694565 755898 232192 698842 967766 204387 787230 213357 795864 619867 861358 762489 912931 615315 527389 747003 637697 599874 169699 984683 912824 285297 572243 246943 606458 295662 686056 664748 866592 602155 326461 413176 376043 847076 437357 703193 269227 305301 825661 085380 030551 417143 585800 101674 875617 434350 879566 416331 692872 097644 500023 714985 999462 219072 786351 905155 445012 773393 563539 068451 576382 815945 370010 303145 566720 745560 086913 455278 379136 641249 941979 899973 294151 819150 582905 876027 808514 827393 324576 710002 230670 938296 238540 648626 550867 406693 329000 632931 539925 388937 063000 845074 411060 309200 018185 980968 617613 078878 899011 254465 871723 457928 255315 615945 972002 468294 196581 110561 989099 768358 783621 018545 942477 306602 362194 150057 457670 170890 302619 710364 742614 206785 668577 754121 166894 335817 589411 496677 254303 887668 371964 780376 642666 588032 289442 863438 969803 782834 806968 039996 186302 911137 871296 210979 270474 572933 986777 291844 842146 116493 986663 238221 465370 614103 799152 629952 582409 526345 699919 708214 153353 405616 828333 242665 877321 404950 141133 151844 819901 275843 797656 116165 294472 652120 199277 247822 348265 181373 914468 766487 037059 592536 644244 842732 211096 654728 112551 478710 320448 904791 123424 307181 488778 350634 043001 136592 369946 122990 097194 502248 603570 947986 363605 168981 809238 552683 198617 544650 383147 752791 338801 544368 683904 872763 164132 324129 111679 880673 624064 / 2591 > 42769 [i]
- extracting embedded OOA [i] would yield OOA(42769, 555, S4, 5, 2590), but