MinT - Best Known (104−64, 104, s)-Nets in Base 5

Best Known (104−64, 104, s)-Nets in Base 5

(104−64, 104, 78)-Net over F₅ — Constructive and digital

Digital (40, 104, 78)-net over F₅, using

t-expansion [i] based on digital (38, 104, 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]

(104−64, 104, 574)-Net in Base 5 — Upper bound on s

There is no (40, 104, 575)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 061427 120219 369903 186084 537264 127684 587665 993625 257657 108445 527872 552833 > 5¹⁰⁴ [i]