Best Known (83, 83+40, s)-Nets in Base 2
(83, 83+40, 68)-Net over F2 — Constructive and digital
Digital (83, 123, 68)-net over F2, using
- 1 times m-reduction [i] based on digital (83, 124, 68)-net over F2, using
- trace code for nets [i] based on digital (21, 62, 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, 62, 34)-net over F4, using
(83, 83+40, 100)-Net over F2 — Digital
Digital (83, 123, 100)-net over F2, using
(83, 83+40, 560)-Net in Base 2 — Upper bound on s
There is no (83, 123, 561)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 10 682012 934587 660144 112875 851144 724824 > 2123 [i]