Best Known (239−84, 239, s)-Nets in Base 3
(239−84, 239, 162)-Net over F3 — Constructive and digital
Digital (155, 239, 162)-net over F3, using
- 7 times m-reduction [i] based on digital (155, 246, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 123, 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, 123, 81)-net over F9, using
(239−84, 239, 317)-Net over F3 — Digital
Digital (155, 239, 317)-net over F3, using
(239−84, 239, 4242)-Net in Base 3 — Upper bound on s
There is no (155, 239, 4243)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1 083121 201246 971626 284955 947508 180610 834486 453910 564466 551188 705957 065243 912047 898739 371532 005043 535831 723052 972085 > 3239 [i]