Best Known (52, 52+41, s)-Nets in Base 2
(52, 52+41, 36)-Net over F2 — Constructive and digital
Digital (52, 93, 36)-net over F2, using
- t-expansion [i] based on digital (51, 93, 36)-net over F2, using
- net from sequence [i] based on digital (51, 35)-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 3 places 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 (51, 35)-sequence over F2, using
(52, 52+41, 41)-Net over F2 — Digital
Digital (52, 93, 41)-net over F2, using
(52, 52+41, 173)-Net in Base 2 — Upper bound on s
There is no (52, 93, 174)-net in base 2, because
- 1 times m-reduction [i] would yield (52, 92, 174)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 5095 429440 058973 171201 078246 > 292 [i]