MinT - Best Known (42, 94, s)-Nets in Base 5

Best Known (42, 94, s)-Nets in Base 5

(42, 94, 78)-Net over F₅ — Constructive and digital

Digital (42, 94, 78)-net over F₅, using

t-expansion [i] based on digital (38, 94, 78)-net over F₅, using
- net from sequence [i] based on digital (38, 77)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
    - an explicitly constructive algebraic function field [i]

(42, 94, 80)-Net over F₅ — Digital

Digital (42, 94, 80)-net over F₅, using

t-expansion [i] based on digital (41, 94, 80)-net over F₅, using
- net from sequence [i] based on digital (41, 79)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 41 and N(F) ≥ 80, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(42, 94, 868)-Net in Base 5 — Upper bound on s

There is no (42, 94, 869)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 506803 511236 076065 406853 587831 082890 654565 975736 592283 272516 268217 > 5⁹⁴ [i]