Best Known (62, ∞, s)-Nets in Base 9
(62, ∞, 81)-Net over F9 — Constructive and digital
Digital (62, m, 81)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (62, 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
(62, ∞, 192)-Net over F9 — Digital
Digital (62, m, 192)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (62, 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
(62, ∞, 522)-Net in Base 9 — Upper bound on s
There is no (62, m, 523)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (62, 1565, 523)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(91565, 523, S9, 3, 1503), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 28 688849 636792 753185 269641 591497 754754 733991 753581 898797 241672 801817 551834 187537 728571 341613 196422 175228 859423 186339 549869 271928 148477 365131 092025 395952 122483 191728 412222 160492 264809 358152 748684 073117 404928 043361 146014 259314 571302 485392 994162 392189 282905 795358 923860 700513 565780 538404 807014 732974 199811 959885 381990 329960 012922 225290 637385 147022 198304 891085 425858 226765 784050 299018 928537 474162 068374 104391 261529 477822 405643 892646 572632 169292 695021 658967 790409 986877 473433 181669 998913 172680 894335 438946 752597 735201 943992 520538 558677 674679 399793 445549 706673 350476 371362 200318 157188 434448 920218 436683 948094 129580 673243 452752 169100 155833 335891 313707 305803 329758 706748 012943 970503 166505 995452 758527 834560 127177 676953 600148 804966 946775 976357 465788 957857 832234 632252 319036 598742 697127 859429 909930 869589 264038 971402 538419 959357 382757 295504 704952 767106 033651 820287 566915 808901 722361 181795 930277 632522 205048 915467 215804 701985 270157 596940 990025 212832 055279 862461 594817 885475 130283 602903 000412 892400 428458 193160 998576 181569 414812 928904 493111 762427 379259 207874 325143 137132 707860 998822 244459 678697 826042 040359 405693 747155 913794 073765 339929 564455 541704 350219 985015 350653 007577 558308 756352 084689 194517 126510 109085 463822 986476 205175 597410 320200 178746 594178 575111 153484 812392 788220 204873 573627 958263 730369 838464 755790 709224 235759 676803 928000 755439 355822 976144 544201 409347 675104 587395 143266 395373 044222 607183 775115 135905 847681 391269 196170 456840 042514 201542 346249 036400 784969 445141 731949 809098 334609 403775 991579 879933 / 94 > 91565 [i]
- extracting embedded OOA [i] would yield OOA(91565, 523, S9, 3, 1503), but