Best Known (112, 158, s)-Nets in Base 2
(112, 158, 112)-Net over F2 — Constructive and digital
Digital (112, 158, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 79, 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
(112, 158, 158)-Net over F2 — Digital
Digital (112, 158, 158)-net over F2, using
(112, 158, 1069)-Net in Base 2 — Upper bound on s
There is no (112, 158, 1070)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 372855 826358 913048 201797 623011 982745 051854 164592 > 2158 [i]