MinT - Best Known (42, 138, s)-Nets in Base 5

Best Known (42, 138, s)-Nets in Base 5

(42, 138, 78)-Net over F₅ — Constructive and digital

Digital (42, 138, 78)-net over F₅, using

t-expansion [i] based on digital (38, 138, 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, 138, 80)-Net over F₅ — Digital

Digital (42, 138, 80)-net over F₅, using

t-expansion [i] based on digital (41, 138, 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, 138, 444)-Net in Base 5 — Upper bound on s

There is no (42, 138, 445)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3 069591 909999 227339 666205 517836 631795 743862 202524 796668 058607 834480 910784 828732 512388 860671 397185 > 5¹³⁸ [i]