Best Known (126, 126+42, s)-Nets in Base 2
(126, 126+42, 195)-Net over F2 — Constructive and digital
Digital (126, 168, 195)-net over F2, using
- trace code for nets [i] based on digital (14, 56, 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
(126, 126+42, 244)-Net over F2 — Digital
Digital (126, 168, 244)-net over F2, using
(126, 126+42, 2191)-Net in Base 2 — Upper bound on s
There is no (126, 168, 2192)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 377 209195 998491 051791 473439 581790 320406 447366 944936 > 2168 [i]