MinT - Best Known (134−37, 134, s)-Nets in Base 5

Best Known (134−37, 134, s)-Nets in Base 5

(134−37, 134, 408)-Net over F₅ — Constructive and digital

Digital (97, 134, 408)-net over F₅, using

trace code for nets [i] based on digital (30, 67, 204)-net over F₂₅, using
- net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
    - a function field by GarcÃa and Quoos [i]

(134−37, 134, 1445)-Net over F₅ — Digital

Digital (97, 134, 1445)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−37, 134, 275842)-Net in Base 5 — Upper bound on s

There is no (97, 134, 275843)-net in base 5, because

1 times m-reduction [i] would yield (97, 133, 275843)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 918 380467 753809 111967 632331 943552 618673 244287 115760 455163 666160 432813 228057 949420 353515 683385 > 5¹³³ [i]