Best Known (245, ∞, s)-Nets in Base 3
(245, ∞, 118)-Net over F3 — Constructive and digital
Digital (245, m, 118)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (245, 117)-sequence over F3, using
- base reduction for sequences [i] based on digital (64, 117)-sequence over F9, using
- s-reduction based on digital (64, 164)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- T4 from the second tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- s-reduction based on digital (64, 164)-sequence over F9, using
- base reduction for sequences [i] based on digital (64, 117)-sequence over F9, using
(245, ∞, 163)-Net over F3 — Digital
Digital (245, m, 163)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (245, 162)-sequence over F3, using
- t-expansion [i] based on digital (151, 162)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 151 and N(F) ≥ 163, using
- t-expansion [i] based on digital (151, 162)-sequence over F3, using
(245, ∞, 505)-Net in Base 3 — Upper bound on s
There is no (245, m, 506)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (245, 3028, 506)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(33028, 506, S3, 6, 2783), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 18 872416 270340 563130 926871 908793 507538 316162 932493 582189 803619 138502 503464 201596 971120 763356 201343 720019 369507 704898 408218 660802 382997 387712 975499 271449 805544 962569 076084 523751 557050 442097 914607 226996 695256 804545 184183 997221 675673 956724 626663 577751 539505 391717 794420 632372 231513 288686 623391 489489 075580 363166 651498 346772 047002 204044 636856 634115 536521 514264 502455 444175 475730 120883 040470 024529 940929 238555 672642 327629 723299 708014 862811 615767 688622 792600 244188 408971 366000 786537 880697 377512 488028 251189 163048 971630 947656 467473 962271 993434 774022 742915 127641 966696 563486 138137 977622 647094 582927 590781 483459 436329 491785 478708 911423 082409 306121 966282 650786 597522 850668 986976 833381 007976 409202 350153 714341 917092 309225 734502 998446 459280 929393 953333 605171 017134 760844 938919 548894 734416 601408 297835 240570 209557 761059 874546 187087 318833 428546 755213 083791 240907 019239 379014 023573 295236 742599 070563 083696 687502 855484 144688 607485 789887 986120 076364 851813 651306 003881 585502 536726 271041 829734 444024 870784 991319 793303 530186 425514 775316 079090 659226 514610 750397 151308 814190 554007 773081 174035 091319 582291 246438 635996 662700 403740 010691 785995 926661 172676 578531 733578 057024 309129 555478 881332 873241 385904 778532 233581 055730 749535 973605 705844 541477 531409 245332 517945 851956 312095 845144 947878 891228 601213 625892 397220 848076 121543 162425 859919 165323 306625 184973 826779 381179 497282 228133 554330 780197 141790 333879 158163 338520 707593 106828 750717 209883 805573 525594 218518 482611 257722 241077 / 232 > 33028 [i]
- extracting embedded OOA [i] would yield OOA(33028, 506, S3, 6, 2783), but