MinT - Best Known (136−37, 136, s)-Nets in Base 5

Best Known (136−37, 136, s)-Nets in Base 5

(136−37, 136, 408)-Net over F₅ — Constructive and digital

Digital (99, 136, 408)-net over F₅, using

2 times m-reduction [i] based on digital (99, 138, 408)-net over F₅, using
- trace code for nets [i] based on digital (30, 69, 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]

(136−37, 136, 1578)-Net over F₅ — Digital

Digital (99, 136, 1578)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−37, 136, 329858)-Net in Base 5 — Upper bound on s

There is no (99, 136, 329859)-net in base 5, because

1 times m-reduction [i] would yield (99, 135, 329859)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 22959 212289 860679 614532 546533 271956 555860 454502 161745 018375 674359 232843 872990 080905 605327 502905 > 5¹³⁵ [i]