Best Known (43, 43+∞, s)-Nets in Base 9
(43, 43+∞, 81)-Net over F9 — Constructive and digital
Digital (43, m, 81)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (43, 80)-sequence over F9, using
- t-expansion [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
- t-expansion [i] based on digital (32, 80)-sequence over F9, using
(43, 43+∞, 147)-Net over F9 — Digital
Digital (43, m, 147)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (43, 146)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 43 and N(F) ≥ 147, using
(43, 43+∞, 369)-Net in Base 9 — Upper bound on s
There is no (43, m, 370)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (43, 1106, 370)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(91106, 370, S9, 3, 1063), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 37 749123 373781 943941 161415 257303 899850 218884 500595 093635 670934 987717 143505 483128 247091 689027 556831 868956 236273 267683 734255 189022 993334 267143 394124 618423 805914 825990 355668 317394 686952 644731 098362 726326 610941 032384 016520 733643 088767 391632 802823 753202 629400 112939 446783 875594 572748 697507 948830 429833 855763 177185 180741 126907 779653 077936 646181 657941 424971 251900 208042 621665 895764 988055 286854 725469 120544 405116 099921 285779 328413 265031 557177 530985 857560 042780 457411 018463 534187 112007 344662 407204 016151 131797 607433 875505 573100 886338 066885 149373 007354 035788 116646 204173 995962 143146 846747 303104 978851 436410 536636 275359 868398 601088 518968 175979 078885 174209 404865 586993 763232 850821 127066 442403 091573 211734 166738 977394 637327 582861 756604 142667 481195 201371 442127 329265 810894 292389 328267 884759 156598 818283 387173 861964 962206 507807 670722 448243 238918 614370 449094 918450 937387 751052 210745 482313 511018 009809 803230 203883 203368 893368 312417 766691 568324 695877 711365 955757 792869 191326 633064 150371 046871 852781 600285 835289 660353 777921 019935 054821 859454 228024 222771 723218 105189 658287 242473 / 133 > 91106 [i]
- extracting embedded OOA [i] would yield OOA(91106, 370, S9, 3, 1063), but