Best Known (92, 92+53, s)-Nets in Base 4
(92, 92+53, 139)-Net over F4 — Constructive and digital
Digital (92, 145, 139)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (1, 27, 9)-net over F4, using
- net from sequence [i] based on digital (1, 8)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- the Hermitian function field over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 1 and N(F) ≥ 9, using
- net from sequence [i] based on digital (1, 8)-sequence over F4, using
- digital (65, 118, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 59, 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, 59, 65)-net over F16, using
- digital (1, 27, 9)-net over F4, using
(92, 92+53, 301)-Net over F4 — Digital
Digital (92, 145, 301)-net over F4, using
(92, 92+53, 7576)-Net in Base 4 — Upper bound on s
There is no (92, 145, 7577)-net in base 4, because
- 1 times m-reduction [i] would yield (92, 144, 7577)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 498 803048 494038 759114 157064 924874 086232 403462 318849 503159 309832 827920 826241 149585 761296 > 4144 [i]