MinT - Best Known (130−90, 130, s)-Nets in Base 5

Best Known (130−90, 130, s)-Nets in Base 5

(130−90, 130, 78)-Net over F₅ — Constructive and digital

Digital (40, 130, 78)-net over F₅, using

t-expansion [i] based on digital (38, 130, 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]

(130−90, 130, 428)-Net in Base 5 — Upper bound on s

There is no (40, 130, 429)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7 933825 037880 088212 738493 446897 189735 820382 126919 413462 580213 911620 631872 215627 823429 882565 > 5¹³⁰ [i]