MinT - Best Known (68−34, 68, s)-Nets in Base 5

Best Known (68−34, 68, s)-Nets in Base 5

(68−34, 68, 72)-Net over F₅ — Constructive and digital

Digital (34, 68, 72)-net over F₅, using

t-expansion [i] based on digital (31, 68, 72)-net over F₅, using
- net from sequence [i] based on digital (31, 71)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 31 and N(F) ≥ 72, using
    - an explicitly constructive algebraic function field [i]

(68−34, 68, 77)-Net over F₅ — Digital

Digital (34, 68, 77)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(68−34, 68, 1109)-Net in Base 5 — Upper bound on s

There is no (34, 68, 1110)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 342891 658709 963919 318877 316453 192087 727702 041945 > 5⁶⁸ [i]