Best Known (161−60, 161, s)-Nets in Base 4
(161−60, 161, 130)-Net over F4 — Constructive and digital
Digital (101, 161, 130)-net over F4, using
- 29 times m-reduction [i] based on digital (101, 190, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 95, 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, 95, 65)-net over F16, using
(161−60, 161, 309)-Net over F4 — Digital
Digital (101, 161, 309)-net over F4, using
(161−60, 161, 6810)-Net in Base 4 — Upper bound on s
There is no (101, 161, 6811)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 8 570811 865646 508925 447425 839290 697387 825119 634494 192015 534592 808296 293338 457229 678528 036151 386080 > 4161 [i]