Best Known (249−54, 249, s)-Nets in Base 2
(249−54, 249, 260)-Net over F2 — Constructive and digital
Digital (195, 249, 260)-net over F2, using
- 3 times m-reduction [i] based on digital (195, 252, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 63, 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, 63, 65)-net over F16, using
(249−54, 249, 492)-Net over F2 — Digital
Digital (195, 249, 492)-net over F2, using
(249−54, 249, 6484)-Net in Base 2 — Upper bound on s
There is no (195, 249, 6485)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 904 669975 585422 583567 826822 341059 102344 305058 736015 238604 047856 091955 586816 > 2249 [i]