Best Known (75, ∞, s)-Nets in Base 3
(75, ∞, 50)-Net over F3 — Constructive and digital
Digital (75, m, 50)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (75, 49)-sequence over F3, using
- base reduction for sequences [i] based on digital (13, 49)-sequence over F9, using
- s-reduction based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- s-reduction based on digital (13, 63)-sequence over F9, using
- base reduction for sequences [i] based on digital (13, 49)-sequence over F9, using
(75, ∞, 84)-Net over F3 — Digital
Digital (75, m, 84)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (75, 83)-sequence over F3, using
- t-expansion [i] based on digital (71, 83)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 71 and N(F) ≥ 84, using
- t-expansion [i] based on digital (71, 83)-sequence over F3, using
(75, ∞, 162)-Net in Base 3 — Upper bound on s
There is no (75, m, 163)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (75, 809, 163)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3809, 163, S3, 5, 734), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 27725 635137 448930 738593 497388 700478 515425 486347 503076 874900 210706 992950 593147 142778 515796 251100 073117 421633 974898 638675 986213 076730 102898 075015 285538 477110 117764 602499 576185 748644 955570 370372 786717 100465 301077 285605 690589 747421 174991 319889 444609 851134 421242 592435 187863 290120 144217 609110 945372 497108 812616 161565 751434 574352 987033 148088 793500 375956 575397 105453 729517 639666 477760 401444 434289 / 245 > 3809 [i]
- extracting embedded OOA [i] would yield OOA(3809, 163, S3, 5, 734), but