Best Known (66, ∞, s)-Nets in Base 9
(66, ∞, 165)-Net over F9 — Constructive and digital
Digital (66, m, 165)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (66, 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
(66, ∞, 192)-Net over F9 — Digital
Digital (66, m, 192)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (66, 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
(66, ∞, 554)-Net in Base 9 — Upper bound on s
There is no (66, m, 555)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (66, 1661, 555)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(91661, 555, S9, 3, 1595), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1518 796576 517511 899469 125147 114645 595510 899885 006733 025302 375823 099878 250296 830959 490239 559645 795362 959461 706575 808490 055246 928891 588568 486824 006859 514765 461014 917162 094225 947909 672090 582078 296790 902824 708722 576034 994110 877108 244785 049440 419769 801586 279800 097954 064284 032839 909550 371249 924915 207598 751291 779998 139253 744885 037781 928308 268841 033363 114714 966361 341663 810496 087824 350662 715199 796131 535467 890014 961080 763428 705290 566802 868478 572208 566336 668984 078830 601795 849665 908889 358412 773327 832575 894736 382613 266158 286310 469961 983076 338676 816025 732942 874798 346768 983506 748762 945371 249381 278793 956317 691865 982922 223049 657850 559192 180283 390262 643091 293225 099007 223374 524989 427141 910342 700848 567311 733230 129109 277549 638243 186186 937332 509328 461343 943958 530355 002197 310616 985012 410698 261824 040012 337673 250743 549551 613457 282166 914064 427204 096345 445641 165769 084238 416927 614018 723032 001168 172797 875870 108702 488713 565446 089368 867124 714882 278710 742346 042081 774958 126713 261625 983664 968951 132487 648611 506620 496326 648105 506284 644991 763532 380025 784912 557585 856249 234638 145464 698568 101201 326116 156513 832791 055573 488552 503701 600440 509503 465691 801996 885769 772556 823391 170048 234083 472145 494345 027580 080548 060374 328489 122225 358001 828661 248243 406326 048867 677565 811715 794533 913178 105849 606992 513153 558746 396429 714961 290066 195201 025993 368367 189497 609500 499300 787466 958980 034226 367005 337409 252563 410415 498021 474178 945059 830507 449262 223264 629711 349487 305235 109465 613016 737515 808372 053802 191698 507083 667855 386390 648552 495998 695837 334222 440078 905470 194277 218031 063531 954491 092563 646380 477230 616058 385465 579162 122177 / 133 > 91661 [i]
- extracting embedded OOA [i] would yield OOA(91661, 555, S9, 3, 1595), but