Best Known (135−44, 135, s)-Nets in Base 3
(135−44, 135, 156)-Net over F3 — Constructive and digital
Digital (91, 135, 156)-net over F3, using
- 3 times m-reduction [i] based on digital (91, 138, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 69, 78)-net over F9, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- trace code for nets [i] based on digital (22, 69, 78)-net over F9, using
(135−44, 135, 245)-Net over F3 — Digital
Digital (91, 135, 245)-net over F3, using
(135−44, 135, 3812)-Net in Base 3 — Upper bound on s
There is no (91, 135, 3813)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 25903 614457 173036 127760 760675 064625 869281 140946 925088 823056 293953 > 3135 [i]