Best Known (129−52, 129, s)-Nets in Base 5
(129−52, 129, 252)-Net over F5 — Constructive and digital
Digital (77, 129, 252)-net over F5, using
- 5 times m-reduction [i] based on digital (77, 134, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 67, 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, 67, 126)-net over F25, using
(129−52, 129, 274)-Net over F5 — Digital
Digital (77, 129, 274)-net over F5, using
(129−52, 129, 7729)-Net in Base 5 — Upper bound on s
There is no (77, 129, 7730)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 1 473342 012664 968986 127210 273555 126366 372833 384888 928244 227753 899830 522012 729512 019373 268161 > 5129 [i]