Best Known (64−52, 64, s)-Nets in Base 25
(64−52, 64, 126)-Net over F25 — Constructive and digital
Digital (12, 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
(64−52, 64, 1200)-Net in Base 25 — Upper bound on s
There is no (12, 64, 1201)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 298305 329395 241937 844587 948710 476576 881047 810096 017369 509353 627090 695399 772955 076288 795825 > 2564 [i]