MinT - Best Known (114−57, 114, s)-Nets in Base 5

Best Known (114−57, 114, s)-Nets in Base 5

(114−57, 114, 82)-Net over F₅ — Constructive and digital

Digital (57, 114, 82)-net over F₅, using

t-expansion [i] based on 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]

(114−57, 114, 116)-Net over F₅ — Digital

Digital (57, 114, 116)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(114−57, 114, 1849)-Net in Base 5 — Upper bound on s

There is no (57, 114, 1850)-net in base 5, because

1 times m-reduction [i] would yield (57, 113, 1850)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 9 723748 877058 762960 921991 647244 635756 961677 755392 992937 795757 030993 270219 638977 > 5¹¹³ [i]