Best Known (31, 173, s)-Nets in Base 8
(31, 173, 65)-Net over F8 — Constructive and digital
Digital (31, 173, 65)-net over F8, using
- t-expansion [i] based on digital (14, 173, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
(31, 173, 97)-Net over F8 — Digital
Digital (31, 173, 97)-net over F8, using
- t-expansion [i] based on digital (28, 173, 97)-net over F8, using
- net from sequence [i] based on digital (28, 96)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 28 and N(F) ≥ 97, using
- net from sequence [i] based on digital (28, 96)-sequence over F8, using
(31, 173, 573)-Net in Base 8 — Upper bound on s
There is no (31, 173, 574)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 1 742907 888749 843214 857673 030173 458525 903799 313673 664688 256043 305769 167016 941619 982937 298784 595846 610211 283808 956414 900189 609894 033646 227792 569001 032898 089248 > 8173 [i]