Best Known (257−152, 257, s)-Nets in Base 2
(257−152, 257, 56)-Net over F2 — Constructive and digital
Digital (105, 257, 56)-net over F2, using
- net from sequence [i] based on digital (105, 55)-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 7 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]
(257−152, 257, 65)-Net over F2 — Digital
Digital (105, 257, 65)-net over F2, using
- t-expansion [i] based on digital (95, 257, 65)-net over F2, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 95 and N(F) ≥ 65, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
(257−152, 257, 206)-Net in Base 2 — Upper bound on s
There is no (105, 257, 207)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 286404 526061 499291 287411 570961 420120 770798 307924 729040 491978 939342 181672 324909 > 2257 [i]