Best Known (82, 82+38, s)-Nets in Base 3
(82, 82+38, 156)-Net over F3 — Constructive and digital
Digital (82, 120, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 60, 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
(82, 82+38, 243)-Net over F3 — Digital
Digital (82, 120, 243)-net over F3, using
(82, 82+38, 4070)-Net in Base 3 — Upper bound on s
There is no (82, 120, 4071)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1803 594195 128003 051999 776819 828561 856760 437612 971338 078331 > 3120 [i]