Best Known (222−74, 222, s)-Nets in Base 3
(222−74, 222, 162)-Net over F3 — Constructive and digital
Digital (148, 222, 162)-net over F3, using
- 10 times m-reduction [i] based on digital (148, 232, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 116, 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, 116, 81)-net over F9, using
(222−74, 222, 348)-Net over F3 — Digital
Digital (148, 222, 348)-net over F3, using
(222−74, 222, 5304)-Net in Base 3 — Upper bound on s
There is no (148, 222, 5305)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 8367 589579 857501 606858 443101 113849 883986 941484 959642 938580 373050 564223 454758 531134 920098 978679 959790 673763 > 3222 [i]