Best Known (183−94, 183, s)-Nets in Base 2
(183−94, 183, 52)-Net over F2 — Constructive and digital
Digital (89, 183, 52)-net over F2, using
- t-expansion [i] based on digital (85, 183, 52)-net over F2, using
- net from sequence [i] based on digital (85, 51)-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 3 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 (85, 51)-sequence over F2, using
(183−94, 183, 57)-Net over F2 — Digital
Digital (89, 183, 57)-net over F2, using
- t-expansion [i] based on digital (83, 183, 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
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
(183−94, 183, 189)-Net over F2 — Upper bound on s (digital)
There is no digital (89, 183, 190)-net over F2, because
- 4 times m-reduction [i] would yield digital (89, 179, 190)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(2179, 190, F2, 90) (dual of [190, 11, 91]-code), but
- residual code [i] would yield linear OA(289, 99, F2, 45) (dual of [99, 10, 46]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(2179, 190, F2, 90) (dual of [190, 11, 91]-code), but
(183−94, 183, 210)-Net in Base 2 — Upper bound on s
There is no (89, 183, 211)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 14 029890 325356 732280 845101 748857 531595 955855 617066 477840 > 2183 [i]