MinT - Best Known (43, 43+38, s)-Nets in Base 5

Best Known (43, 43+38, s)-Nets in Base 5

(43, 43+38, 78)-Net over F₅ — Constructive and digital

Digital (43, 81, 78)-net over F₅, using

t-expansion [i] based on digital (38, 81, 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]

(43, 43+38, 110)-Net over F₅ — Digital

Digital (43, 81, 110)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(43, 43+38, 1878)-Net in Base 5 — Upper bound on s

There is no (43, 81, 1879)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 415 585100 221232 780353 586418 108668 501279 773699 055768 063125 > 5⁸¹ [i]