Best Known (127−81, 127, s)-Nets in Base 2
(127−81, 127, 34)-Net over F2 — Constructive and digital
Digital (46, 127, 34)-net over F2, using
- t-expansion [i] based on digital (45, 127, 34)-net over F2, using
- net from sequence [i] based on digital (45, 33)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 1 place with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (45, 33)-sequence over F2, using
(127−81, 127, 89)-Net in Base 2 — Upper bound on s
There is no (46, 127, 90)-net in base 2, because
- 1 times m-reduction [i] would yield (46, 126, 90)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 86 681080 045762 966184 531069 644163 309350 > 2126 [i]