MinT - Best Known (88−41, 88, s)-Nets in Base 5

Best Known (88−41, 88, s)-Nets in Base 5

(88−41, 88, 104)-Net over F₅ — Constructive and digital

Digital (47, 88, 104)-net over F₅, using

trace code for nets [i] based on digital (3, 44, 52)-net over F₂₅, using
- net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
    - a function field by GarcÃa and Quoos [i]

(88−41, 88, 120)-Net over F₅ — Digital

Digital (47, 88, 120)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−41, 88, 2264)-Net in Base 5 — Upper bound on s

There is no (47, 88, 2265)-net in base 5, because

1 times m-reduction [i] would yield (47, 87, 2265)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6 482469 542478 361089 570799 740787 519897 189875 025370 840783 199025 > 5⁸⁷ [i]