Best Known (175−48, 175, s)-Nets in Base 2
(175−48, 175, 138)-Net over F2 — Constructive and digital
Digital (127, 175, 138)-net over F2, using
- 21 times duplication [i] based on digital (126, 174, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 58, 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, 58, 46)-net over F8, using
(175−48, 175, 198)-Net over F2 — Digital
Digital (127, 175, 198)-net over F2, using
(175−48, 175, 1500)-Net in Base 2 — Upper bound on s
There is no (127, 175, 1501)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 48035 934544 597906 392779 942085 111651 015614 395670 508191 > 2175 [i]