Best Known (122, 122+62, s)-Nets in Base 3
(122, 122+62, 156)-Net over F3 — Constructive and digital
Digital (122, 184, 156)-net over F3, using
- 16 times m-reduction [i] based on digital (122, 200, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 100, 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, 100, 78)-net over F9, using
(122, 122+62, 287)-Net over F3 — Digital
Digital (122, 184, 287)-net over F3, using
(122, 122+62, 4186)-Net in Base 3 — Upper bound on s
There is no (122, 184, 4187)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 6213 307890 687093 378943 663416 725046 161116 438577 491122 142504 315419 915882 375655 108470 495795 > 3184 [i]