Best Known (100, 165, s)-Nets in Base 2
(100, 165, 66)-Net over F2 — Constructive and digital
Digital (100, 165, 66)-net over F2, using
- 5 times m-reduction [i] based on digital (100, 170, 66)-net over F2, using
- trace code for nets [i] based on digital (15, 85, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- trace code for nets [i] based on digital (15, 85, 33)-net over F4, using
(100, 165, 82)-Net over F2 — Digital
Digital (100, 165, 82)-net over F2, using
(100, 165, 401)-Net in Base 2 — Upper bound on s
There is no (100, 165, 402)-net in base 2, because
- 1 times m-reduction [i] would yield (100, 164, 402)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 25 099485 825071 780734 540255 790748 377170 748459 492508 > 2164 [i]