MinT - Best Known (107−54, 107, s)-Nets in Base 5

Best Known (107−54, 107, s)-Nets in Base 5

(107−54, 107, 82)-Net over F₅ — Constructive and digital

Digital (53, 107, 82)-net over F₅, using

t-expansion [i] based on digital (48, 107, 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]

(107−54, 107, 106)-Net over F₅ — Digital

Digital (53, 107, 106)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(107−54, 107, 1588)-Net in Base 5 — Upper bound on s

There is no (53, 107, 1589)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 621 151388 028122 434069 966172 106531 223603 970298 890208 365166 760127 779027 583661 > 5¹⁰⁷ [i]