Best Known (131−52, 131, s)-Nets in Base 5
(131−52, 131, 252)-Net over F5 — Constructive and digital
Digital (79, 131, 252)-net over F5, using
- 7 times m-reduction [i] based on digital (79, 138, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 69, 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, 69, 126)-net over F25, using
(131−52, 131, 293)-Net over F5 — Digital
Digital (79, 131, 293)-net over F5, using
(131−52, 131, 8750)-Net in Base 5 — Upper bound on s
There is no (79, 131, 8751)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 36 805367 288565 555307 687454 817570 075908 872490 895267 784576 782245 145516 218203 239055 617359 817625 > 5131 [i]