Best Known (102−40, 102, s)-Nets in Base 5
(102−40, 102, 252)-Net over F5 — Constructive and digital
Digital (62, 102, 252)-net over F5, using
- 2 times m-reduction [i] based on digital (62, 104, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 52, 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, 52, 126)-net over F25, using
(102−40, 102, 253)-Net over F5 — Digital
Digital (62, 102, 253)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(5102, 253, F5, 2, 40) (dual of [(253, 2), 404, 41]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(5100, 252, F5, 2, 40) (dual of [(252, 2), 404, 41]-NRT-code), using
- extracting embedded OOA [i] based on digital (60, 100, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 50, 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, 50, 126)-net over F25, using
- extracting embedded OOA [i] based on digital (60, 100, 252)-net over F5, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(5100, 252, F5, 2, 40) (dual of [(252, 2), 404, 41]-NRT-code), using
(102−40, 102, 7606)-Net in Base 5 — Upper bound on s
There is no (62, 102, 7607)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 197639 130709 559855 250770 749131 475547 845422 956005 288748 971941 115202 667185 > 5102 [i]