Best Known (128−28, 128, s)-Nets in Base 5
(128−28, 128, 504)-Net over F5 — Constructive and digital
Digital (100, 128, 504)-net over F5, using
- 2 times m-reduction [i] based on digital (100, 130, 504)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (35, 50, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 25, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- trace code for nets [i] based on digital (10, 25, 126)-net over F25, using
- digital (50, 80, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 40, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25 (see above)
- trace code for nets [i] based on digital (10, 40, 126)-net over F25, using
- digital (35, 50, 252)-net over F5, using
- (u, u+v)-construction [i] based on
(128−28, 128, 5636)-Net over F5 — Digital
Digital (100, 128, 5636)-net over F5, using
(128−28, 128, 3715176)-Net in Base 5 — Upper bound on s
There is no (100, 128, 3715177)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 293873 905121 734508 615791 097560 464040 564323 465689 279379 870367 235066 791317 720707 017850 882025 > 5128 [i]