Best Known (55, 55+53, s)-Nets in Base 8
(55, 55+53, 160)-Net over F8 — Constructive and digital
Digital (55, 108, 160)-net over F8, using
- trace code for nets [i] based on digital (1, 54, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
(55, 55+53, 201)-Net over F8 — Digital
Digital (55, 108, 201)-net over F8, using
(55, 55+53, 7831)-Net in Base 8 — Upper bound on s
There is no (55, 108, 7832)-net in base 8, because
- 1 times m-reduction [i] would yield (55, 107, 7832)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 4 275208 554719 376687 925834 519510 577148 908713 382487 694390 904240 767306 922198 175387 282885 009111 700400 > 8107 [i]