Best Known (84, 84+40, s)-Nets in Base 3
(84, 84+40, 156)-Net over F3 — Constructive and digital
Digital (84, 124, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 62, 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
(84, 84+40, 236)-Net over F3 — Digital
Digital (84, 124, 236)-net over F3, using
(84, 84+40, 3751)-Net in Base 3 — Upper bound on s
There is no (84, 124, 3752)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 146103 507812 947512 906406 039465 335409 033833 743769 567674 070081 > 3124 [i]