MinT - Best Known (48, 114, s)-Nets in Base 5

Best Known (48, 114, s)-Nets in Base 5

(48, 114, 82)-Net over F₅ — Constructive and digital

Digital (48, 114, 82)-net over F₅, using

net from sequence [i] based on digital (48, 81)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 48 and N(F) ≥ 82, using
  - an explicitly constructive algebraic function field [i]

(48, 114, 92)-Net over F₅ — Digital

Digital (48, 114, 92)-net over F₅, using

t-expansion [i] based on digital (47, 114, 92)-net over F₅, using
- net from sequence [i] based on digital (47, 91)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 47 and N(F) ≥ 92, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(48, 114, 830)-Net in Base 5 — Upper bound on s

There is no (48, 114, 831)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 48 339258 750037 839776 353509 780853 626238 616853 945184 550872 827201 046515 886731 955325 > 5¹¹⁴ [i]