MinT - Best Known (91−45, 91, s)-Nets in Base 5

Best Known (91−45, 91, s)-Nets in Base 5

(91−45, 91, 78)-Net over F₅ — Constructive and digital

Digital (46, 91, 78)-net over F₅, using

t-expansion [i] based on digital (38, 91, 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]

(91−45, 91, 100)-Net over F₅ — Digital

Digital (46, 91, 100)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(91−45, 91, 1621)-Net in Base 5 — Upper bound on s

There is no (46, 91, 1622)-net in base 5, because

1 times m-reduction [i] would yield (46, 90, 1622)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 811 207148 051048 002711 348137 289831 578966 990171 819635 344846 835265 > 5⁹⁰ [i]