Best Known (11, ∞, s)-Nets in Base 7
(11, ∞, 19)-Net over F7 — Constructive and digital
Digital (11, m, 19)-net over F7 for arbitrarily large m, using
- net from sequence [i] based on digital (11, 18)-sequence over F7, using
(11, ∞, 38)-Net over F7 — Digital
Digital (11, m, 38)-net over F7 for arbitrarily large m, using
- net from sequence [i] based on digital (11, 37)-sequence over F7, using
- t-expansion [i] based on digital (9, 37)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 9 and N(F) ≥ 38, using
- t-expansion [i] based on digital (9, 37)-sequence over F7, using
(11, ∞, 82)-Net in Base 7 — Upper bound on s
There is no (11, m, 83)-net in base 7 for arbitrarily large m, because
- m-reduction [i] would yield (11, 163, 83)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7163, 83, S7, 2, 152), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 11 835859 933879 651892 576153 957238 792240 080254 933375 367749 393514 926892 794094 745159 685194 095824 462886 799654 218773 301668 178947 835203 321689 895203 / 17 > 7163 [i]
- extracting embedded OOA [i] would yield OOA(7163, 83, S7, 2, 152), but