Best Known (66, 124, s)-Nets in Base 2
(66, 124, 43)-Net over F2 — Constructive and digital
Digital (66, 124, 43)-net over F2, using
- t-expansion [i] based on digital (59, 124, 43)-net over F2, using
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
(66, 124, 48)-Net over F2 — Digital
Digital (66, 124, 48)-net over F2, using
- t-expansion [i] based on digital (65, 124, 48)-net over F2, using
- net from sequence [i] based on digital (65, 47)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 65 and N(F) ≥ 48, using
- net from sequence [i] based on digital (65, 47)-sequence over F2, using
(66, 124, 165)-Net over F2 — Upper bound on s (digital)
There is no digital (66, 124, 166)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(2124, 166, F2, 58) (dual of [166, 42, 59]-code), but
- construction Y1 [i] would yield
- OA(2123, 150, S2, 58), but
- the linear programming bound shows that M ≥ 36000 467012 365704 432940 148948 904738 978722 217984 / 3201 323125 > 2123 [i]
- OA(242, 166, S2, 16), but
- discarding factors would yield OA(242, 146, S2, 16), but
- the Rao or (dual) Hamming bound shows that M ≥ 4 467697 956730 > 242 [i]
- discarding factors would yield OA(242, 146, S2, 16), but
- OA(2123, 150, S2, 58), but
- construction Y1 [i] would yield
(66, 124, 186)-Net in Base 2 — Upper bound on s
There is no (66, 124, 187)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 22 765626 897036 575690 075424 768676 037072 > 2124 [i]