Best Known (189−49, 189, s)-Nets in Base 2
(189−49, 189, 195)-Net over F2 — Constructive and digital
Digital (140, 189, 195)-net over F2, using
- trace code for nets [i] based on digital (14, 63, 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
(189−49, 189, 243)-Net over F2 — Digital
Digital (140, 189, 243)-net over F2, using
(189−49, 189, 2200)-Net in Base 2 — Upper bound on s
There is no (140, 189, 2201)-net in base 2, because
- 1 times m-reduction [i] would yield (140, 188, 2201)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 394 238234 431033 789756 782961 604500 875270 883049 216928 207721 > 2188 [i]