Best Known (222−137, 222, s)-Nets in Base 2
(222−137, 222, 52)-Net over F2 — Constructive and digital
Digital (85, 222, 52)-net over F2, using
- net from sequence [i] based on digital (85, 51)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 3 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
(222−137, 222, 57)-Net over F2 — Digital
Digital (85, 222, 57)-net over F2, using
- t-expansion [i] based on digital (83, 222, 57)-net over F2, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 83 and N(F) ≥ 57, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
(222−137, 222, 162)-Net in Base 2 — Upper bound on s
There is no (85, 222, 163)-net in base 2, because
- 1 times m-reduction [i] would yield (85, 221, 163)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 3 425861 073854 504985 661430 469423 396476 639149 964328 115044 753191 687872 > 2221 [i]