Best Known (257−143, 257, s)-Nets in Base 2
(257−143, 257, 57)-Net over F2 — Constructive and digital
Digital (114, 257, 57)-net over F2, using
- t-expansion [i] based on digital (110, 257, 57)-net over F2, using
- net from sequence [i] based on digital (110, 56)-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 8 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]
- net from sequence [i] based on digital (110, 56)-sequence over F2, using
(257−143, 257, 73)-Net over F2 — Digital
Digital (114, 257, 73)-net over F2, using
- net from sequence [i] based on digital (114, 72)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 114 and N(F) ≥ 73, using
(257−143, 257, 239)-Net in Base 2 — Upper bound on s
There is no (114, 257, 240)-net in base 2, because
- 1 times m-reduction [i] would yield (114, 256, 240)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 139460 848391 819989 255005 262831 753625 239330 535870 855841 694041 280899 347009 202389 > 2256 [i]