Best Known (156, 156+∞, s)-Nets in Base 4
(156, 156+∞, 130)-Net over F4 — Constructive and digital
Digital (156, m, 130)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (156, 129)-sequence over F4, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 from the second 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) = 105 and N(F) ≥ 130, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
(156, 156+∞, 215)-Net over F4 — Digital
Digital (156, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (156, 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
(156, 156+∞, 485)-Net in Base 4 — Upper bound on s
There is no (156, m, 486)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (156, 2424, 486)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42424, 486, S4, 5, 2268), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 85307 307759 300259 941171 350663 901618 065203 308938 271815 793619 867601 176775 123561 211644 723600 878769 508432 110970 135517 229413 939400 921592 767253 571893 877558 003968 001871 211474 888310 657972 412844 901191 460008 873892 556195 965246 299625 046512 245315 160597 265498 519887 768150 117024 942165 600022 771239 622388 036730 031803 627816 767520 064095 264697 815700 061704 499568 365707 192217 225946 853417 125212 925950 317743 088076 858524 631780 586164 309475 176130 437203 030083 788368 406959 063077 046510 527274 774259 108535 104681 549889 107418 023840 640340 764228 846434 045276 982090 606916 344502 278086 138911 760973 892109 114898 821837 626401 544547 262921 139260 492830 396048 838161 077361 576497 929816 512262 962898 054442 874784 339434 447323 147867 037467 675059 701423 944444 572598 434763 970215 893601 400415 200108 828122 966546 127079 062832 120272 161248 800240 753369 267080 187600 271653 587871 019303 482198 294615 843126 975359 890264 352600 903148 206920 797642 674523 677882 275281 596341 385283 452336 359842 845587 264260 822473 049212 613245 771973 423118 432475 702905 135937 582605 495332 834922 730572 584145 197491 701091 510121 485957 558543 040896 482616 016546 779069 471726 162759 819341 470514 207113 822106 785042 544094 881865 720660 720560 707687 530207 436091 658264 813799 112882 687870 650700 922982 948226 295418 531720 567603 244550 168188 454373 864446 737375 586482 016411 973204 596273 785210 448093 659617 017063 207934 862256 891549 059766 476886 609246 899979 947550 697014 547964 789254 828073 477677 157243 603255 354625 685930 255247 299478 213961 059171 515722 905382 999021 292682 044058 267013 267237 521972 586126 245888 / 2269 > 42424 [i]
- extracting embedded OOA [i] would yield OOA(42424, 486, S4, 5, 2268), but