MinT - Best Known (88−45, 88, s)-Nets in Base 5

Best Known (88−45, 88, s)-Nets in Base 5

(88−45, 88, 78)-Net over F₅ — Constructive and digital

Digital (43, 88, 78)-net over F₅, using

t-expansion [i] based on digital (38, 88, 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]

(88−45, 88, 87)-Net over F₅ — Digital

Digital (43, 88, 87)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−45, 88, 1298)-Net in Base 5 — Upper bound on s

There is no (43, 88, 1299)-net in base 5, because

1 times m-reduction [i] would yield (43, 87, 1299)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6 462680 491403 138436 759825 731568 857166 733536 633010 956310 687913 > 5⁸⁷ [i]