MinT - Best Known (88, 137, s)-Nets in Base 5

Best Known (88, 137, s)-Nets in Base 5

(88, 137, 296)-Net over F₅ — Constructive and digital

Digital (88, 137, 296)-net over F₅, using

1 times m-reduction [i] based on digital (88, 138, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 69, 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]

(88, 137, 456)-Net over F₅ — Digital

Digital (88, 137, 456)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 137, 22376)-Net in Base 5 — Upper bound on s

There is no (88, 137, 22377)-net in base 5, because

1 times m-reduction [i] would yield (88, 136, 22377)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 114848 340049 825905 007146 532821 260960 835519 942589 988206 964103 346287 206014 503302 901737 248896 414625 > 5¹³⁶ [i]