MinT - Best Known (116−39, 116, s)-Nets in Base 5

Best Known (116−39, 116, s)-Nets in Base 5

(116−39, 116, 296)-Net over F₅ — Constructive and digital

Digital (77, 116, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 58, 148)-net over F₂₅, using
- net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
    - a function field by GarcÃa and Quoos [i]

(116−39, 116, 522)-Net over F₅ — Digital

Digital (77, 116, 522)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(116−39, 116, 33696)-Net in Base 5 — Upper bound on s

There is no (77, 116, 33697)-net in base 5, because

1 times m-reduction [i] would yield (77, 115, 33697)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 240 793411 313025 818713 775418 441932 919225 176191 038487 011401 087825 731015 253983 851965 > 5¹¹⁵ [i]