MinT - Best Known (93−44, 93, s)-Nets in Base 5

Best Known (93−44, 93, s)-Nets in Base 5

(93−44, 93, 82)-Net over F₅ — Constructive and digital

Digital (49, 93, 82)-net over F₅, using

t-expansion [i] based on digital (48, 93, 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]

(93−44, 93, 118)-Net over F₅ — Digital

Digital (49, 93, 118)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(93−44, 93, 2023)-Net in Base 5 — Upper bound on s

There is no (49, 93, 2024)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 101439 187676 146928 051837 828178 153143 967217 348263 612212 081255 990913 > 5⁹³ [i]