Best Known (106−42, 106, s)-Nets in Base 5
(106−42, 106, 252)-Net over F5 — Constructive and digital
Digital (64, 106, 252)-net over F5, using
- 2 times m-reduction [i] based on digital (64, 108, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 54, 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, 54, 126)-net over F25, using
(106−42, 106, 253)-Net over F5 — Digital
Digital (64, 106, 253)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(5106, 253, F5, 2, 42) (dual of [(253, 2), 400, 43]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(5104, 252, F5, 2, 42) (dual of [(252, 2), 400, 43]-NRT-code), using
- extracting embedded OOA [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
- extracting embedded OOA [i] based on digital (62, 104, 252)-net over F5, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(5104, 252, F5, 2, 42) (dual of [(252, 2), 400, 43]-NRT-code), using
(106−42, 106, 7305)-Net in Base 5 — Upper bound on s
There is no (64, 106, 7306)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 123 364900 532505 051798 082038 121623 621057 817236 594069 478753 438223 413907 933225 > 5106 [i]