MinT - Best Known (122−41, 122, s)-Nets in Base 5

Best Known (122−41, 122, s)-Nets in Base 5

(122−41, 122, 296)-Net over F₅ — Constructive and digital

Digital (81, 122, 296)-net over F₅, using

2 times m-reduction [i] based on digital (81, 124, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 62, 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]

(122−41, 122, 543)-Net over F₅ — Digital

Digital (81, 122, 543)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−41, 122, 35142)-Net in Base 5 — Upper bound on s

There is no (81, 122, 35143)-net in base 5, because

1 times m-reduction [i] would yield (81, 121, 35143)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3 762135 075814 255849 174885 251547 124473 818823 496251 345290 486538 927482 933779 437707 650225 > 5¹²¹ [i]