Best Known (138, 138+48, s)-Nets in Base 2
(138, 138+48, 195)-Net over F2 — Constructive and digital
Digital (138, 186, 195)-net over F2, using
- trace code for nets [i] based on digital (14, 62, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
(138, 138+48, 243)-Net over F2 — Digital
Digital (138, 186, 243)-net over F2, using
(138, 138+48, 2075)-Net in Base 2 — Upper bound on s
There is no (138, 186, 2076)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 99 116707 215350 814397 478807 098809 797473 203111 508725 949421 > 2186 [i]