MinT - Best Known (109−54, 109, s)-Nets in Base 5

Best Known (109−54, 109, s)-Nets in Base 5

(109−54, 109, 82)-Net over F₅ — Constructive and digital

Digital (55, 109, 82)-net over F₅, using

t-expansion [i] based on digital (48, 109, 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]

(109−54, 109, 115)-Net over F₅ — Digital

Digital (55, 109, 115)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−54, 109, 1792)-Net in Base 5 — Upper bound on s

There is no (55, 109, 1793)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 15604 995207 929379 748528 771986 920577 476816 565782 362151 718139 724068 488204 858269 > 5¹⁰⁹ [i]