Best Known (149, ∞, s)-Nets in Base 3
(149, ∞, 81)-Net over F3 — Constructive and digital
Digital (149, m, 81)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (149, 80)-sequence over F3, using
- t-expansion [i] based on digital (144, 80)-sequence over F3, using
- base reduction for sequences [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- base reduction for sequences [i] based on digital (32, 80)-sequence over F9, using
- t-expansion [i] based on digital (144, 80)-sequence over F3, using
(149, ∞, 120)-Net over F3 — Digital
Digital (149, m, 120)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (149, 119)-sequence over F3, using
- t-expansion [i] based on digital (113, 119)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 113 and N(F) ≥ 120, using
- t-expansion [i] based on digital (113, 119)-sequence over F3, using
(149, ∞, 311)-Net in Base 3 — Upper bound on s
There is no (149, m, 312)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (149, 1865, 312)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31865, 312, S3, 6, 1716), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 116524 146044 296530 127404 105324 372727 573628 124440 395990 761766 809386 984470 248207 116425 259443 656731 022117 499796 448888 691990 851887 069434 495243 478868 824573 899901 836594 712175 547702 743049 729314 261346 033779 283965 490586 849420 268078 013978 313460 176055 891924 395625 684429 563147 917520 689954 892134 900079 396277 682431 882977 641004 402897 473458 361097 983018 475174 206698 970351 516022 116919 992317 750222 891324 787914 964668 460233 591438 640660 695867 468947 760955 162456 400747 315411 089800 924497 200497 878750 084373 489974 970181 178768 787399 182910 469685 451168 290372 063860 315727 302166 698243 303369 568310 932895 923737 699504 618009 182653 851589 303139 014628 118005 027029 590811 347549 692994 715064 879134 879555 710698 296995 973186 063076 955821 206236 296480 152128 019186 446858 685533 410223 934941 688010 097425 410807 615566 292675 504093 025803 939951 815553 678337 010353 768655 127000 464394 967679 363765 063849 548078 392937 354904 983888 544515 135339 782512 535390 754117 / 1717 > 31865 [i]
- extracting embedded OOA [i] would yield OOA(31865, 312, S3, 6, 1716), but