Best Known (251−168, 251, s)-Nets in Base 2
(251−168, 251, 51)-Net over F2 — Constructive and digital
Digital (83, 251, 51)-net over F2, using
- t-expansion [i] based on digital (80, 251, 51)-net over F2, using
- net from sequence [i] based on digital (80, 50)-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 2 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]
- net from sequence [i] based on digital (80, 50)-sequence over F2, using
(251−168, 251, 57)-Net over F2 — Digital
Digital (83, 251, 57)-net over F2, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 83 and N(F) ≥ 57, using
(251−168, 251, 120)-Net in Base 2 — Upper bound on s
There is no (83, 251, 121)-net in base 2, because
- 17 times m-reduction [i] would yield (83, 234, 121)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2234, 121, S2, 2, 151), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 662567 649291 894123 593736 562778 594443 435306 461328 357109 295602 325484 732416 / 19 > 2234 [i]
- extracting embedded OOA [i] would yield OOA(2234, 121, S2, 2, 151), but