Best Known (168, 168+47, s)-Nets in Base 2
(168, 168+47, 260)-Net over F2 — Constructive and digital
Digital (168, 215, 260)-net over F2, using
- 1 times m-reduction [i] based on digital (168, 216, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 54, 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, 54, 65)-net over F16, using
(168, 168+47, 425)-Net over F2 — Digital
Digital (168, 215, 425)-net over F2, using
(168, 168+47, 5927)-Net in Base 2 — Upper bound on s
There is no (168, 215, 5928)-net in base 2, because
- 1 times m-reduction [i] would yield (168, 214, 5928)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 26385 968513 929783 844991 283479 004531 068608 308671 235155 646175 305458 > 2214 [i]