Best Known (216−62, 216, s)-Nets in Base 2
(216−62, 216, 138)-Net over F2 — Constructive and digital
Digital (154, 216, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 72, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
(216−62, 216, 212)-Net over F2 — Digital
Digital (154, 216, 212)-net over F2, using
(216−62, 216, 1508)-Net in Base 2 — Upper bound on s
There is no (154, 216, 1509)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 105514 054714 090063 173580 857875 534586 412232 798083 517607 587280 828960 > 2216 [i]