MinT - Best Known (115−75, 115, s)-Nets in Base 5

Best Known (115−75, 115, s)-Nets in Base 5

(115−75, 115, 78)-Net over F₅ — Constructive and digital

Digital (40, 115, 78)-net over F₅, using

t-expansion [i] based on digital (38, 115, 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]

(115−75, 115, 494)-Net in Base 5 — Upper bound on s

There is no (40, 115, 495)-net in base 5, because

1 times m-reduction [i] would yield (40, 114, 495)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 48 276546 024935 899380 110552 332220 772202 316069 908721 787869 641464 287443 688738 898733 > 5¹¹⁴ [i]