MinT - Best Known (115−38, 115, s)-Nets in Base 5

Best Known (115−38, 115, s)-Nets in Base 5

(115−38, 115, 296)-Net over F₅ — Constructive and digital

Digital (77, 115, 296)-net over F₅, using

1 times m-reduction [i] based on 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]

(115−38, 115, 561)-Net over F₅ — Digital

Digital (77, 115, 561)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(115−38, 115, 33696)-Net in Base 5 — Upper bound on s

There is no (77, 115, 33697)-net in base 5, because

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]