Best Known (64−50, 64, s)-Nets in Base 25
(64−50, 64, 126)-Net over F25 — Constructive and digital
Digital (14, 64, 126)-net over F25, using
- t-expansion [i] based on digital (10, 64, 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
(64−50, 64, 130)-Net over F25 — Digital
Digital (14, 64, 130)-net over F25, using
- net from sequence [i] based on digital (14, 129)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 14 and N(F) ≥ 130, using
(64−50, 64, 1594)-Net in Base 25 — Upper bound on s
There is no (14, 64, 1595)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 296417 774295 953677 380883 017473 333555 791964 574632 003199 607824 142496 047178 416532 651825 178697 > 2564 [i]