Best Known (159, 159+93, s)-Nets in Base 2
(159, 159+93, 112)-Net over F2 — Constructive and digital
Digital (159, 252, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 126, 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
(159, 159+93, 135)-Net over F2 — Digital
Digital (159, 252, 135)-net over F2, using
(159, 159+93, 724)-Net in Base 2 — Upper bound on s
There is no (159, 252, 725)-net in base 2, because
- 1 times m-reduction [i] would yield (159, 251, 725)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 3742 424160 505864 348323 486198 722962 541945 837287 526862 448534 812933 383019 600960 > 2251 [i]