Best Known (199, 199+51, s)-Nets in Base 2
(199, 199+51, 260)-Net over F2 — Constructive and digital
Digital (199, 250, 260)-net over F2, using
- t-expansion [i] based on digital (198, 250, 260)-net over F2, using
- 6 times m-reduction [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
- 6 times m-reduction [i] based on digital (198, 256, 260)-net over F2, using
(199, 199+51, 589)-Net over F2 — Digital
Digital (199, 250, 589)-net over F2, using
(199, 199+51, 10099)-Net in Base 2 — Upper bound on s
There is no (199, 250, 10100)-net in base 2, because
- 1 times m-reduction [i] would yield (199, 249, 10100)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 905 783664 104541 207728 493137 812431 600488 063638 069488 783260 058100 656486 579780 > 2249 [i]