Best Known (37, 37+∞, s)-Nets in Base 5
(37, 37+∞, 72)-Net over F5 — Constructive and digital
Digital (37, m, 72)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (37, 71)-sequence over F5, using
- t-expansion [i] based on digital (31, 71)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 31 and N(F) ≥ 72, using
- t-expansion [i] based on digital (31, 71)-sequence over F5, using
(37, 37+∞, 76)-Net over F5 — Digital
Digital (37, m, 76)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (37, 75)-sequence over F5, using
- t-expansion [i] based on digital (34, 75)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 34 and N(F) ≥ 76, using
- t-expansion [i] based on digital (34, 75)-sequence over F5, using
(37, 37+∞, 164)-Net in Base 5 — Upper bound on s
There is no (37, m, 165)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (37, 491, 165)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5491, 165, S5, 3, 454), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1798 746530 828567 236792 205466 724178 101636 000333 648985 939700 559869 784824 509697 755405 494853 540031 599366 397648 089905 986067 061051 152098 291162 401380 046377 641500 453414 570538 810285 455388 334554 696940 373123 040760 303677 289682 483565 003994 936521 635699 589687 008276 752304 335309 798689 501408 021360 042389 891795 733418 669209 734142 011569 701935 513876 378536 224365 234375 / 91 > 5491 [i]
- extracting embedded OOA [i] would yield OOA(5491, 165, S5, 3, 454), but