Best Known (117, 117+53, s)-Nets in Base 3
(117, 117+53, 162)-Net over F3 — Constructive and digital
Digital (117, 170, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 85, 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
(117, 117+53, 341)-Net over F3 — Digital
Digital (117, 170, 341)-net over F3, using
(117, 117+53, 6635)-Net in Base 3 — Upper bound on s
There is no (117, 170, 6636)-net in base 3, because
- 1 times m-reduction [i] would yield (117, 169, 6636)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 430 491584 317884 375903 668617 955872 775770 854754 654492 818899 134581 705015 566298 229929 > 3169 [i]