Best Known (161, 161+65, s)-Nets in Base 4
(161, 161+65, 531)-Net over F4 — Constructive and digital
Digital (161, 226, 531)-net over F4, using
- 5 times m-reduction [i] based on digital (161, 231, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 77, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 77, 177)-net over F64, using
(161, 161+65, 1099)-Net over F4 — Digital
Digital (161, 226, 1099)-net over F4, using
(161, 161+65, 72918)-Net in Base 4 — Upper bound on s
There is no (161, 226, 72919)-net in base 4, because
- 1 times m-reduction [i] would yield (161, 225, 72919)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2908 013284 294907 335831 005253 417001 058910 549145 056181 252307 072155 887516 671676 977173 680244 247713 660992 126013 166399 337064 106913 886208 363190 > 4225 [i]