Best Known (257−58, 257, s)-Nets in Base 2
(257−58, 257, 260)-Net over F2 — Constructive and digital
Digital (199, 257, 260)-net over F2, using
- 21 times duplication [i] based on digital (198, 256, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 64, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 64, 65)-net over F16, using
(257−58, 257, 454)-Net over F2 — Digital
Digital (199, 257, 454)-net over F2, using
(257−58, 257, 5388)-Net in Base 2 — Upper bound on s
There is no (199, 257, 5389)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 232773 972839 462367 187304 533413 534241 785673 238171 388636 099891 974406 142667 585184 > 2257 [i]