Best Known (177, 177+73, s)-Nets in Base 2
(177, 177+73, 138)-Net over F2 — Constructive and digital
Digital (177, 250, 138)-net over F2, using
- 21 times duplication [i] based on digital (176, 249, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 83, 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, 83, 46)-net over F8, using
(177, 177+73, 230)-Net over F2 — Digital
Digital (177, 250, 230)-net over F2, using
(177, 177+73, 1672)-Net in Base 2 — Upper bound on s
There is no (177, 250, 1673)-net in base 2, because
- 1 times m-reduction [i] would yield (177, 249, 1673)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 913 464809 210939 106947 476799 201368 957380 113268 546326 292058 252662 083564 563272 > 2249 [i]