Best Known (156, 156+88, s)-Nets in Base 3
(156, 156+88, 162)-Net over F3 — Constructive and digital
Digital (156, 244, 162)-net over F3, using
- 4 times m-reduction [i] based on digital (156, 248, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 124, 81)-net over F9, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- trace code for nets [i] based on digital (32, 124, 81)-net over F9, using
(156, 156+88, 300)-Net over F3 — Digital
Digital (156, 244, 300)-net over F3, using
(156, 156+88, 3773)-Net in Base 3 — Upper bound on s
There is no (156, 244, 3774)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 261 799674 958930 976981 889472 445012 609391 597803 376539 484672 073920 827774 180660 726182 754870 855052 430261 624131 351785 014809 > 3244 [i]