Best Known (27, ∞, s)-Nets in Base 5
(27, ∞, 51)-Net over F5 — Constructive and digital
Digital (27, m, 51)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (27, 50)-sequence over F5, using
- t-expansion [i] based on digital (22, 50)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 22 and N(F) ≥ 51, using
- t-expansion [i] based on digital (22, 50)-sequence over F5, using
(27, ∞, 55)-Net over F5 — Digital
Digital (27, m, 55)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (27, 54)-sequence over F5, using
- t-expansion [i] based on digital (23, 54)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 23 and N(F) ≥ 55, using
- t-expansion [i] based on digital (23, 54)-sequence over F5, using
(27, ∞, 123)-Net in Base 5 — Upper bound on s
There is no (27, m, 124)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (27, 368, 124)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5368, 124, S5, 3, 341), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 39 086740 718824 821061 674321 223363 967942 888680 959492 585008 491670 764996 331045 125185 626054 049518 590971 560851 615180 296779 236897 684636 662120 597104 457547 386316 537720 543535 263769 450297 257153 190758 796139 405240 853298 116499 673904 404577 040594 404024 886898 696422 576904 296875 / 171 > 5368 [i]
- extracting embedded OOA [i] would yield OOA(5368, 124, S5, 3, 341), but