Best Known (71, 71+40, s)-Nets in Base 5
(71, 71+40, 252)-Net over F5 — Constructive and digital
Digital (71, 111, 252)-net over F5, using
- 11 times m-reduction [i] based on digital (71, 122, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 61, 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, 61, 126)-net over F25, using
(71, 71+40, 374)-Net over F5 — Digital
Digital (71, 111, 374)-net over F5, using
(71, 71+40, 15708)-Net in Base 5 — Upper bound on s
There is no (71, 111, 15709)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 385528 990267 678711 862167 487242 084910 710855 833295 772662 650817 900849 539979 303345 > 5111 [i]