Best Known (110, 110+104, s)-Nets in Base 2
(110, 110+104, 57)-Net over F2 — Constructive and digital
Digital (110, 214, 57)-net over F2, using
- net from sequence [i] based on digital (110, 56)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 8 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
(110, 110+104, 72)-Net over F2 — Digital
Digital (110, 214, 72)-net over F2, using
- net from sequence [i] based on digital (110, 71)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 110 and N(F) ≥ 72, using
(110, 110+104, 232)-Net in Base 2 — Upper bound on s
There is no (110, 214, 233)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2214, 233, S2, 104), but
- the linear programming bound shows that M ≥ 77186 327308 052281 732131 664194 137202 618623 144481 733659 013399 636143 505408 / 2 304599 > 2214 [i]