MinT - Best Known (137−45, 137, s)-Nets in Base 5

Best Known (137−45, 137, s)-Nets in Base 5

(137−45, 137, 296)-Net over F₅ — Constructive and digital

Digital (92, 137, 296)-net over F₅, using

9 times m-reduction [i] based on digital (92, 146, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 73, 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]

(137−45, 137, 658)-Net over F₅ — Digital

Digital (92, 137, 658)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−45, 137, 47375)-Net in Base 5 — Upper bound on s

There is no (92, 137, 47376)-net in base 5, because

1 times m-reduction [i] would yield (92, 136, 47376)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 114832 186611 926209 807947 985071 322537 992306 706034 931206 950596 378412 318371 097171 805366 981622 586625 > 5¹³⁶ [i]