Best Known (168−56, 168, s)-Nets in Base 2
(168−56, 168, 68)-Net over F2 — Constructive and digital
Digital (112, 168, 68)-net over F2, using
- 14 times m-reduction [i] based on digital (112, 182, 68)-net over F2, using
- trace code for nets [i] based on digital (21, 91, 34)-net over F4, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- T5 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- trace code for nets [i] based on digital (21, 91, 34)-net over F4, using
(168−56, 168, 84)-Net in Base 2 — Constructive
(112, 168, 84)-net in base 2, using
- 2 times m-reduction [i] based on (112, 170, 84)-net in base 2, using
- trace code for nets [i] based on (27, 85, 42)-net in base 4, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- base expansion [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
- base expansion [i] based on digital (54, 41)-sequence over F2, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- trace code for nets [i] based on (27, 85, 42)-net in base 4, using
(168−56, 168, 121)-Net over F2 — Digital
Digital (112, 168, 121)-net over F2, using
(168−56, 168, 682)-Net in Base 2 — Upper bound on s
There is no (112, 168, 683)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 379 508120 419219 337822 520547 815960 724307 531241 876072 > 2168 [i]