Best Known (123−48, 123, s)-Nets in Base 5
(123−48, 123, 252)-Net over F5 — Constructive and digital
Digital (75, 123, 252)-net over F5, using
- 7 times m-reduction [i] based on digital (75, 130, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 65, 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, 65, 126)-net over F25, using
(123−48, 123, 296)-Net over F5 — Digital
Digital (75, 123, 296)-net over F5, using
(123−48, 123, 9347)-Net in Base 5 — Upper bound on s
There is no (75, 123, 9348)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 94 072844 085121 812176 428103 519727 746675 999871 404798 301551 597927 101408 267304 967952 743425 > 5123 [i]