Best Known (51, 76, s)-Nets in Base 2
(51, 76, 60)-Net over F2 — Constructive and digital
Digital (51, 76, 60)-net over F2, using
- trace code for nets [i] based on digital (13, 38, 30)-net over F4, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 13 and N(F) ≥ 30, using
- F4 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) = 13 and N(F) ≥ 30, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
(51, 76, 68)-Net over F2 — Digital
Digital (51, 76, 68)-net over F2, using
(51, 76, 385)-Net in Base 2 — Upper bound on s
There is no (51, 76, 386)-net in base 2, because
- 1 times m-reduction [i] would yield (51, 75, 386)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 38500 385305 834562 967392 > 275 [i]