Best Known (88, ∞, s)-Nets in Base 9
(88, ∞, 222)-Net over F9 — Constructive and digital
Digital (88, m, 222)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (88, 221)-sequence over F9, using
- t-expansion [i] based on digital (79, 221)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 79 and N(F) ≥ 222, using
- F4 from the 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) = 79 and N(F) ≥ 222, using
- t-expansion [i] based on digital (79, 221)-sequence over F9, using
(88, ∞, 245)-Net over F9 — Digital
Digital (88, m, 245)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (88, 244)-sequence over F9, using
- t-expansion [i] based on digital (81, 244)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 81 and N(F) ≥ 245, using
- t-expansion [i] based on digital (81, 244)-sequence over F9, using
(88, ∞, 731)-Net in Base 9 — Upper bound on s
There is no (88, m, 732)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (88, 2192, 732)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(92192, 732, S9, 3, 2104), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 12 302286 802283 114570 458892 376750 212282 584541 161936 390160 240745 145090 379601 516733 594370 905033 394421 323612 716061 513211 858630 267927 553985 975935 052094 798733 811980 856893 198671 533928 891710 807842 174048 597146 188213 244561 850123 724916 692002 284835 625538 458232 878433 031615 580450 663122 951763 915320 085541 870928 607615 197231 894782 588872 264950 795984 835320 895396 200026 695720 421259 840692 841062 433604 234753 736350 317669 501159 247434 250762 639698 121560 730212 098621 840190 402890 415347 272374 080850 849686 302152 579782 386450 786488 029311 543588 315669 420648 445655 480622 357218 011978 243427 641646 656193 384612 227849 815515 041237 208043 570631 290611 377796 091152 685619 445148 738395 222295 269260 795641 894057 747530 498380 129575 441795 180044 147632 660066 123628 860013 922405 675969 536095 919455 917404 971516 188088 057902 692438 106737 428437 415148 460513 148505 531476 477795 299644 918045 836725 711902 649559 979289 596441 145005 017161 971766 311461 193976 106529 101281 044978 695424 126185 614161 229418 336824 885368 608248 194316 475138 467816 213436 650188 726431 832802 079384 812051 953430 699893 335338 767117 842121 973472 453788 209766 029648 815196 054217 156862 703917 757217 935156 085716 664136 473230 247361 861599 452674 892360 041534 951244 527029 331676 833139 726778 605072 209629 527288 945981 238446 898872 622230 893656 454866 024723 429780 618624 795464 419986 784765 800314 812718 570535 121673 733798 120506 909044 249606 296463 026858 509898 841155 151667 129381 297090 728166 809575 456556 785894 205526 450157 309152 982496 333323 947168 642494 060756 296922 176340 390361 470200 262587 999501 150448 890958 065218 672444 741799 807977 155181 976985 179001 407931 994136 253662 730272 138540 909184 519665 150916 414253 520660 347113 057111 106505 489873 420190 048133 297164 829219 482100 320649 810774 177662 056054 620925 601930 590885 435368 747400 802483 233232 660808 213456 077662 778750 028380 764568 941104 386614 611791 267105 410078 426982 157443 899187 077566 743607 108265 761909 120882 536400 041349 844754 838715 909956 322438 683311 323164 655756 591533 748901 837132 861782 336892 851199 366765 170851 500075 928790 108136 285275 050727 393625 179164 024471 285567 174201 916035 175273 739676 186298 125403 802422 640095 401706 004379 645278 134771 390529 255030 199771 223974 452150 393154 116695 618116 720881 617778 440217 / 2105 > 92192 [i]
- extracting embedded OOA [i] would yield OOA(92192, 732, S9, 3, 2104), but