Best Known (81, 81+39, s)-Nets in Base 2
(81, 81+39, 68)-Net over F2 — Constructive and digital
Digital (81, 120, 68)-net over F2, using
- trace code for nets [i] based on digital (21, 60, 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
(81, 81+39, 98)-Net over F2 — Digital
Digital (81, 120, 98)-net over F2, using
(81, 81+39, 581)-Net in Base 2 — Upper bound on s
There is no (81, 120, 582)-net in base 2, because
- 1 times m-reduction [i] would yield (81, 119, 582)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 673670 150253 485050 070740 203575 732120 > 2119 [i]