Best Known (118, 118+55, s)-Nets in Base 2
(118, 118+55, 76)-Net over F2 — Constructive and digital
Digital (118, 173, 76)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (37, 64, 34)-net over F2, using
- trace code for nets [i] based on digital (5, 32, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- trace code for nets [i] based on digital (5, 32, 17)-net over F4, using
- digital (54, 109, 42)-net over F2, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- digital (37, 64, 34)-net over F2, using
(118, 118+55, 86)-Net in Base 2 — Constructive
(118, 173, 86)-net in base 2, using
- 3 times m-reduction [i] based on (118, 176, 86)-net in base 2, using
- trace code for nets [i] based on (30, 88, 43)-net in base 4, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- t-expansion [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]
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
- trace code for nets [i] based on (30, 88, 43)-net in base 4, using
(118, 118+55, 138)-Net over F2 — Digital
Digital (118, 173, 138)-net over F2, using
(118, 118+55, 864)-Net in Base 2 — Upper bound on s
There is no (118, 173, 865)-net in base 2, because
- 1 times m-reduction [i] would yield (118, 172, 865)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 6057 548067 357155 575856 942327 947583 513745 226972 882336 > 2172 [i]