Best Known (243−54, 243, s)-Nets in Base 2
(243−54, 243, 260)-Net over F2 — Constructive and digital
Digital (189, 243, 260)-net over F2, using
- 1 times m-reduction [i] based on digital (189, 244, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 61, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 61, 65)-net over F16, using
(243−54, 243, 451)-Net over F2 — Digital
Digital (189, 243, 451)-net over F2, using
(243−54, 243, 5553)-Net in Base 2 — Upper bound on s
There is no (189, 243, 5554)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 14 166103 944023 771488 484007 821615 018131 827482 425088 933315 006731 503938 767776 > 2243 [i]