MinT - Best Known (89, 89+41, s)-Nets in Base 5

Best Known (89, 89+41, s)-Nets in Base 5

(89, 89+41, 296)-Net over F₅ — Constructive and digital

Digital (89, 130, 296)-net over F₅, using

10 times m-reduction [i] based on digital (89, 140, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 70, 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]

(89, 89+41, 757)-Net over F₅ — Digital

Digital (89, 130, 757)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 89+41, 66912)-Net in Base 5 — Upper bound on s

There is no (89, 130, 66913)-net in base 5, because

1 times m-reduction [i] would yield (89, 129, 66913)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 469491 630905 472060 197859 014640 292042 140526 699085 918573 509615 975478 150366 657669 853416 577585 > 5¹²⁹ [i]