Best Known (165−45, 165, s)-Nets in Base 2
(165−45, 165, 138)-Net over F2 — Constructive and digital
Digital (120, 165, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 55, 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
(165−45, 165, 191)-Net over F2 — Digital
Digital (120, 165, 191)-net over F2, using
(165−45, 165, 1555)-Net in Base 2 — Upper bound on s
There is no (120, 165, 1556)-net in base 2, because
- 1 times m-reduction [i] would yield (120, 164, 1556)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 23 396331 763402 275619 402725 327820 818228 468608 425392 > 2164 [i]