Best Known (46, 87, s)-Nets in Base 4
(46, 87, 66)-Net over F4 — Constructive and digital
Digital (46, 87, 66)-net over F4, using
- 1 times m-reduction [i] based on digital (46, 88, 66)-net over F4, using
- trace code for nets [i] based on digital (2, 44, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- trace code for nets [i] based on digital (2, 44, 33)-net over F16, using
(46, 87, 87)-Net over F4 — Digital
Digital (46, 87, 87)-net over F4, using
(46, 87, 1058)-Net in Base 4 — Upper bound on s
There is no (46, 87, 1059)-net in base 4, because
- 1 times m-reduction [i] would yield (46, 86, 1059)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 6096 247789 218894 920889 987432 053835 595763 040145 121944 > 486 [i]