Best Known (141, ∞, s)-Nets in Base 4
(141, ∞, 130)-Net over F4 — Constructive and digital
Digital (141, m, 130)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (141, 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
(141, ∞, 176)-Net over F4 — Digital
Digital (141, m, 176)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (141, 175)-sequence over F4, using
- t-expansion [i] based on digital (125, 175)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 125 and N(F) ≥ 176, using
- t-expansion [i] based on digital (125, 175)-sequence over F4, using
(141, ∞, 439)-Net in Base 4 — Upper bound on s
There is no (141, m, 440)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (141, 2194, 440)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42194, 440, S4, 5, 2053), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 8908 729222 274727 249240 856118 893711 156143 343071 078459 534956 877861 336364 795533 122406 196294 487859 667044 628203 116527 312467 786414 901848 303520 193497 214379 829936 199951 668376 100528 858302 601485 082858 085449 462746 774902 885153 085601 603335 001071 886354 880054 618101 880133 748200 309120 564223 750008 128851 009647 153122 246950 288132 360955 460081 480017 291678 178768 491398 357881 608591 768829 656288 622729 818532 184182 791989 710148 873046 613021 927164 793636 642199 587916 228116 807846 893438 538898 404342 253729 001822 836447 445315 447270 105389 684020 501065 228015 950605 643614 647208 186583 723676 176712 808621 104725 470818 475534 997272 687474 651282 090617 470756 197553 629143 997436 403576 488355 854999 799014 451622 729516 863333 676274 163728 224766 707735 945253 680226 618171 262125 694391 635563 058196 339653 485457 190072 601612 079897 149411 333562 031664 495617 383584 258941 084790 545528 683098 312632 592787 015598 659316 686201 344362 705339 138221 683762 196398 643279 218135 109346 177873 961630 521248 405470 049809 605735 504014 677916 256758 385315 441157 869387 643332 853353 208370 656836 939103 103269 131166 443097 915456 175563 307268 914591 508156 022278 829324 007758 328885 916364 691441 010570 214483 474454 709805 387012 529270 627770 460799 943600 015669 692060 573129 019972 608132 674942 935884 529826 364417 407847 500905 143531 758343 581724 216377 137707 886668 377715 755890 131658 911051 771916 067560 299957 813919 106483 598405 082589 311235 484425 388032 / 1027 > 42194 [i]
- extracting embedded OOA [i] would yield OOA(42194, 440, S4, 5, 2053), but