MinT - Best Known (137−94, 137, s)-Nets in Base 5

Best Known (137−94, 137, s)-Nets in Base 5

(137−94, 137, 78)-Net over F₅ — Constructive and digital

Digital (43, 137, 78)-net over F₅, using

t-expansion [i] based on digital (38, 137, 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]

(137−94, 137, 84)-Net over F₅ — Digital

Digital (43, 137, 84)-net over F₅, using

net from sequence [i] based on digital (43, 83)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 43 and N(F) ≥ 84, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(137−94, 137, 466)-Net in Base 5 — Upper bound on s

There is no (43, 137, 467)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 593311 276770 833202 913346 302126 050814 278063 892511 522877 442385 968241 011175 329601 615615 884873 431125 > 5¹³⁷ [i]