Best Known (135, 135+72, s)-Nets in Base 3
(135, 135+72, 156)-Net over F3 — Constructive and digital
Digital (135, 207, 156)-net over F3, using
- 19 times m-reduction [i] based on digital (135, 226, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 113, 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, 113, 78)-net over F9, using
(135, 135+72, 288)-Net over F3 — Digital
Digital (135, 207, 288)-net over F3, using
(135, 135+72, 3919)-Net in Base 3 — Upper bound on s
There is no (135, 207, 3920)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 582 466931 046164 957125 111132 867128 484000 805410 591282 983124 879080 927429 962597 248681 978489 127186 824065 > 3207 [i]