MinT - Best Known (90−43, 90, s)-Nets in Base 5

Best Known (90−43, 90, s)-Nets in Base 5

(90−43, 90, 78)-Net over F₅ — Constructive and digital

Digital (47, 90, 78)-net over F₅, using

t-expansion [i] based on digital (38, 90, 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]

(90−43, 90, 112)-Net over F₅ — Digital

Digital (47, 90, 112)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−43, 90, 1974)-Net in Base 5 — Upper bound on s

There is no (47, 90, 1975)-net in base 5, because

1 times m-reduction [i] would yield (47, 89, 1975)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 162 848435 982453 642127 192664 900138 322819 138589 180917 382381 301901 > 5⁸⁹ [i]