Best Known (21, 21+∞, s)-Nets in Base 9
(21, 21+∞, 74)-Net over F9 — Constructive and digital
Digital (21, m, 74)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (21, 73)-sequence over F9, using
- t-expansion [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- t-expansion [i] based on digital (17, 73)-sequence over F9, using
(21, 21+∞, 88)-Net over F9 — Digital
Digital (21, m, 88)-net over F9 for arbitrarily large m, using
- net from sequence [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
(21, 21+∞, 190)-Net in Base 9 — Upper bound on s
There is no (21, m, 191)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (21, 379, 191)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(9379, 191, S9, 2, 358), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 19242 054699 229712 203468 951058 097184 604086 840946 534425 446499 246609 394508 288900 230293 486492 167640 052989 073519 234870 188545 974568 568727 078306 647336 279207 704256 074004 115857 287434 513248 400489 238739 308563 287089 440850 133541 607479 470795 486694 076030 098502 256299 168253 193115 558310 046526 231331 128681 776699 543139 421637 087768 794564 760314 214924 135663 965018 010793 634247 877022 698447 / 359 > 9379 [i]
- extracting embedded OOA [i] would yield OOA(9379, 191, S9, 2, 358), but