Best Known (171, 171+70, s)-Nets in Base 2
(171, 171+70, 138)-Net over F2 — Constructive and digital
Digital (171, 241, 138)-net over F2, using
- 21 times duplication [i] based on digital (170, 240, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 80, 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, 80, 46)-net over F8, using
(171, 171+70, 226)-Net over F2 — Digital
Digital (171, 241, 226)-net over F2, using
(171, 171+70, 1593)-Net in Base 2 — Upper bound on s
There is no (171, 241, 1594)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 3 580750 714319 651545 083779 321920 377243 372886 749944 539854 564607 201713 729640 > 2241 [i]