Best Known (122−35, 122, s)-Nets in Base 2
(122−35, 122, 84)-Net over F2 — Constructive and digital
Digital (87, 122, 84)-net over F2, using
- 1 times m-reduction [i] based on digital (87, 123, 84)-net over F2, using
- trace code for nets [i] based on digital (5, 41, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- trace code for nets [i] based on digital (5, 41, 28)-net over F8, using
(122−35, 122, 133)-Net over F2 — Digital
Digital (87, 122, 133)-net over F2, using
(122−35, 122, 971)-Net in Base 2 — Upper bound on s
There is no (87, 122, 972)-net in base 2, because
- 1 times m-reduction [i] would yield (87, 121, 972)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 2 658695 397103 670227 869075 402367 398268 > 2121 [i]