Best Known (212−64, 212, s)-Nets in Base 2
(212−64, 212, 112)-Net over F2 — Constructive and digital
Digital (148, 212, 112)-net over F2, using
- 18 times m-reduction [i] based on digital (148, 230, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 115, 56)-net over F4, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- F5 from the 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) = 33 and N(F) ≥ 56, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
- trace code for nets [i] based on digital (33, 115, 56)-net over F4, using
(212−64, 212, 185)-Net over F2 — Digital
Digital (148, 212, 185)-net over F2, using
(212−64, 212, 1215)-Net in Base 2 — Upper bound on s
There is no (148, 212, 1216)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 6628 552656 097743 741977 071414 475876 546125 152770 308696 209014 346295 > 2212 [i]