Best Known (188−62, 188, s)-Nets in Base 3
(188−62, 188, 162)-Net over F3 — Constructive and digital
Digital (126, 188, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 94, 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
(188−62, 188, 312)-Net over F3 — Digital
Digital (126, 188, 312)-net over F3, using
(188−62, 188, 4828)-Net in Base 3 — Upper bound on s
There is no (126, 188, 4829)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 502373 156532 033668 310479 598917 201535 867860 141777 099506 704979 522366 212053 148498 613115 841563 > 3188 [i]