MinT - Best Known (82−42, 82, s)-Nets in Base 5

Best Known (82−42, 82, s)-Nets in Base 5

(82−42, 82, 78)-Net over F₅ — Constructive and digital

Digital (40, 82, 78)-net over F₅, using

t-expansion [i] based on digital (38, 82, 78)-net over F₅, using
- net from sequence [i] based on digital (38, 77)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
    - an explicitly constructive algebraic function field [i]

(82−42, 82, 82)-Net over F₅ — Digital

Digital (40, 82, 82)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(82−42, 82, 1148)-Net in Base 5 — Upper bound on s

There is no (40, 82, 1149)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2095 683482 023221 063175 831565 327788 398333 252705 164573 420517 > 5⁸² [i]