MinT - Best Known (135−37, 135, s)-Nets in Base 5

Best Known (135−37, 135, s)-Nets in Base 5

(135−37, 135, 408)-Net over F₅ — Constructive and digital

Digital (98, 135, 408)-net over F₅, using

1 times m-reduction [i] based on digital (98, 136, 408)-net over F₅, using
- trace code for nets [i] based on digital (30, 68, 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]

(135−37, 135, 1510)-Net over F₅ — Digital

Digital (98, 135, 1510)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−37, 135, 301644)-Net in Base 5 — Upper bound on s

There is no (98, 135, 301645)-net in base 5, because

1 times m-reduction [i] would yield (98, 134, 301645)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4592 044314 358062 194674 435813 697583 781979 101568 368220 954285 908969 026137 426475 233339 792492 266969 > 5¹³⁴ [i]