Best Known (122, 122+56, s)-Nets in Base 3
(122, 122+56, 162)-Net over F3 — Constructive and digital
Digital (122, 178, 162)-net over F3, using
- 2 times m-reduction [i] based on digital (122, 180, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 90, 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, 90, 81)-net over F9, using
(122, 122+56, 345)-Net over F3 — Digital
Digital (122, 178, 345)-net over F3, using
(122, 122+56, 6069)-Net in Base 3 — Upper bound on s
There is no (122, 178, 6070)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 8 488805 335373 335716 670119 089118 570263 035976 434009 413350 111923 795344 422377 037544 039417 > 3178 [i]