Best Known (64, ∞, s)-Nets in Base 9
(64, ∞, 165)-Net over F9 — Constructive and digital
Digital (64, m, 165)-net over F9 for arbitrarily large m, using
- net from sequence [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
(64, ∞, 192)-Net over F9 — Digital
Digital (64, m, 192)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (64, 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
(64, ∞, 538)-Net in Base 9 — Upper bound on s
There is no (64, m, 539)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (64, 1613, 539)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(91613, 539, S9, 3, 1549), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 446263 612955 140008 177001 319837 203100 903670 301853 134432 934946 600778 988152 081136 940040 357390 823961 860832 785961 442105 140144 683500 600990 422245 750904 677409 960335 845566 822593 903378 275548 259273 167042 900635 234956 272712 037550 964887 147381 285119 607775 514389 329290 654241 216652 888950 785114 121668 842769 101713 251397 379022 232432 168750 579421 257168 549306 984745 891326 141846 272162 235814 825788 092651 399891 640829 681803 034563 310883 411006 743278 451010 618855 554799 543965 074477 296421 161616 933905 238502 154636 512019 969425 626181 427125 174169 443596 505429 653055 347240 489421 660394 976389 191546 111521 119196 388116 033140 507513 513659 983978 237961 528624 006959 647658 206457 217798 041988 705709 614193 002861 564566 478027 338225 820109 869127 222139 985370 942220 757157 641425 109692 134078 804156 851834 822709 515400 374592 714423 983691 849598 439162 155181 606785 081977 511166 484183 442252 082372 935787 829136 843789 110526 694218 165862 707375 909643 782110 821842 432645 111833 298686 630582 483375 806273 021339 719538 543626 176804 442433 200020 453589 393440 579403 974150 205927 744684 923914 707879 062221 160908 632142 202756 597301 490180 087996 199503 233345 102829 200016 252556 206733 606483 059492 065754 402547 577678 700305 574931 023515 183352 762544 331906 101943 103207 187643 288869 545374 680832 584685 062839 908363 051747 227824 683899 261713 364166 858173 012718 926213 222201 822712 557459 633697 926015 178175 852166 617686 902178 065302 504293 917047 712357 730775 434159 181993 559540 982963 918269 131801 148870 926764 513337 460506 103933 539665 589181 688018 585159 452220 597461 241411 723828 025722 367094 317415 716438 018621 635885 924311 172542 447116 897387 447708 409861 702027 000186 892983 / 775 > 91613 [i]
- extracting embedded OOA [i] would yield OOA(91613, 539, S9, 3, 1549), but