Best Known (22, ∞, s)-Nets in Base 9
(22, ∞, 78)-Net over F9 — Constructive and digital
Digital (22, m, 78)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 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) = 22 and N(F) ≥ 78, using
(22, ∞, 88)-Net over F9 — Digital
Digital (22, m, 88)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (22, 87)-sequence over F9, using
- t-expansion [i] based on digital (21, 87)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 21 and N(F) ≥ 88, using
- t-expansion [i] based on digital (21, 87)-sequence over F9, using
(22, ∞, 198)-Net in Base 9 — Upper bound on s
There is no (22, m, 199)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (22, 395, 199)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(9395, 199, S9, 2, 373), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 17 448639 662793 068196 353249 913700 521054 024981 923750 530348 209777 366334 225490 918082 529810 808663 906780 554393 741139 229391 884531 720284 969371 758690 010046 234413 764814 257207 386607 372594 438105 884569 687286 523034 706926 571643 372425 314231 066152 217354 760108 275335 488172 034670 736226 618611 381117 942108 463114 298187 740523 963340 142190 045922 864831 985299 089009 840902 169619 460049 913319 930931 430459 301943 / 187 > 9395 [i]
- extracting embedded OOA [i] would yield OOA(9395, 199, S9, 2, 373), but