Best Known (249−69, 249, s)-Nets in Base 2
(249−69, 249, 195)-Net over F2 — Constructive and digital
Digital (180, 249, 195)-net over F2, using
- trace code for nets [i] based on digital (14, 83, 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
(249−69, 249, 260)-Net over F2 — Digital
Digital (180, 249, 260)-net over F2, using
(249−69, 249, 2074)-Net in Base 2 — Upper bound on s
There is no (180, 249, 2075)-net in base 2, because
- 1 times m-reduction [i] would yield (180, 248, 2075)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 456 815788 069724 527824 918184 278932 368072 948450 868599 411710 644286 506142 748224 > 2248 [i]