Best Known (73, 73+∞, s)-Nets in Base 9
(73, 73+∞, 165)-Net over F9 — Constructive and digital
Digital (73, m, 165)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (73, 164)-sequence over F9, using
- t-expansion [i] 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
- t-expansion [i] based on digital (64, 164)-sequence over F9, using
(73, 73+∞, 192)-Net over F9 — Digital
Digital (73, m, 192)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (73, 191)-sequence over F9, using
- t-expansion [i] based on digital (61, 191)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 61 and N(F) ≥ 192, using
- t-expansion [i] based on digital (61, 191)-sequence over F9, using
(73, 73+∞, 610)-Net in Base 9 — Upper bound on s
There is no (73, m, 611)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (73, 1829, 611)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(91829, 611, S9, 3, 1756), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 361 625044 523054 156980 707385 759159 703926 005302 921124 979315 275411 488513 773942 767366 707883 420917 295270 353440 132206 996355 392886 727325 397798 025375 687432 056068 139994 542437 749333 202662 634911 612023 193807 016336 623839 812310 835415 447175 007328 829148 082046 679522 579248 300465 046395 014389 829438 475036 463577 447794 823174 675827 202940 149341 509729 922454 078956 126910 283898 100819 624529 749788 838375 608325 919121 047330 564040 370764 391560 203167 322675 620200 975740 271298 982372 741269 628433 773029 843879 323966 137196 791335 148881 737126 097136 518352 752763 611621 817497 401844 986528 933757 053455 872697 577106 539757 417172 602465 125044 009071 543760 495785 908207 932682 910795 058236 768248 891489 650447 653489 686354 418566 327825 680751 078611 212039 624384 547412 421634 715912 708740 306434 148642 417913 095695 683407 209401 719574 770602 105773 037025 357814 813659 101360 118807 292048 905814 760185 557156 909126 131991 294750 813110 677539 255186 324027 104808 810030 138283 667900 984524 573752 031797 536625 605026 204262 451479 940250 955077 760949 170052 945254 504215 857009 128039 823850 745641 973629 610343 368421 133989 210818 193580 481739 994296 258040 013121 555944 058727 191447 908166 528439 508220 570764 735785 671556 112526 214382 773442 382690 646278 766586 447871 930718 377161 690652 080756 432514 143296 050038 865456 265716 488063 252267 159380 247421 911490 912764 884625 506480 108822 018231 859132 919559 248128 153997 272055 817504 286079 201004 843157 571361 578432 917740 532348 719510 894226 489308 960893 434109 116762 243089 886293 430218 407076 886275 848618 317576 121188 682092 648740 051469 536483 884090 399413 339714 340149 106358 566033 547724 990139 325412 766761 257015 765163 485819 228269 122944 256649 640087 810836 610616 803568 535065 660299 542832 323381 206572 165854 532111 531466 456898 595260 163039 422067 669305 061348 505375 684973 783813 255728 079271 335561 839491 938822 666681 942229 942433 170662 683080 933386 164597 / 1757 > 91829 [i]
- extracting embedded OOA [i] would yield OOA(91829, 611, S9, 3, 1756), but