Best Known (134, 134+51, s)-Nets in Base 2
(134, 134+51, 138)-Net over F2 — Constructive and digital
Digital (134, 185, 138)-net over F2, using
- 1 times m-reduction [i] based on digital (134, 186, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 62, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- trace code for nets [i] based on digital (10, 62, 46)-net over F8, using
(134, 134+51, 205)-Net over F2 — Digital
Digital (134, 185, 205)-net over F2, using
(134, 134+51, 1635)-Net in Base 2 — Upper bound on s
There is no (134, 185, 1636)-net in base 2, because
- 1 times m-reduction [i] would yield (134, 184, 1636)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 24 794482 279995 471308 677052 282246 878109 045266 437208 660612 > 2184 [i]