Best Known (207−59, 207, s)-Nets in Base 2
(207−59, 207, 138)-Net over F2 — Constructive and digital
Digital (148, 207, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 69, 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
(207−59, 207, 208)-Net over F2 — Digital
Digital (148, 207, 208)-net over F2, using
(207−59, 207, 1562)-Net in Base 2 — Upper bound on s
There is no (148, 207, 1563)-net in base 2, because
- 1 times m-reduction [i] would yield (148, 206, 1563)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 103 754964 719944 169193 205109 210067 427860 404443 515046 941332 103536 > 2206 [i]