Best Known (150−111, 150, s)-Nets in Base 8
(150−111, 150, 98)-Net over F8 — Constructive and digital
Digital (39, 150, 98)-net over F8, using
- t-expansion [i] based on digital (37, 150, 98)-net over F8, using
- net from sequence [i] based on digital (37, 97)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 37 and N(F) ≥ 98, using
- net from sequence [i] based on digital (37, 97)-sequence over F8, using
(150−111, 150, 129)-Net over F8 — Digital
Digital (39, 150, 129)-net over F8, using
- t-expansion [i] based on digital (38, 150, 129)-net over F8, using
- net from sequence [i] based on digital (38, 128)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 38 and N(F) ≥ 129, using
- net from sequence [i] based on digital (38, 128)-sequence over F8, using
(150−111, 150, 817)-Net in Base 8 — Upper bound on s
There is no (39, 150, 818)-net in base 8, because
- 1 times m-reduction [i] would yield (39, 149, 818)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 365 597854 430750 393098 324234 870026 343778 377000 525657 688446 420168 499835 426050 153481 820421 106342 791905 981897 280515 445087 853421 662196 215168 > 8149 [i]