Best Known (178−50, 178, s)-Nets in Base 2
(178−50, 178, 135)-Net over F2 — Constructive and digital
Digital (128, 178, 135)-net over F2, using
- 21 times duplication [i] based on digital (127, 177, 135)-net over F2, using
- trace code for nets [i] based on digital (9, 59, 45)-net over F8, using
- net from sequence [i] based on digital (9, 44)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using
- net from sequence [i] based on digital (9, 44)-sequence over F8, using
- trace code for nets [i] based on digital (9, 59, 45)-net over F8, using
(178−50, 178, 189)-Net over F2 — Digital
Digital (128, 178, 189)-net over F2, using
(178−50, 178, 1379)-Net in Base 2 — Upper bound on s
There is no (128, 178, 1380)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 389282 955588 887594 767788 661335 174198 024799 782066 170212 > 2178 [i]