MinT - Best Known (81, 81+33, s)-Nets in Base 5

Best Known (81, 81+33, s)-Nets in Base 5

(81, 81+33, 296)-Net over F₅ — Constructive and digital

Digital (81, 114, 296)-net over F₅, using

10 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]

(81, 81+33, 1004)-Net over F₅ — Digital

Digital (81, 114, 1004)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 81+33, 146865)-Net in Base 5 — Upper bound on s

There is no (81, 114, 146866)-net in base 5, because

1 times m-reduction [i] would yield (81, 113, 146866)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 9 629962 606756 361975 693704 260939 151911 244612 589985 524442 302945 212958 649712 972545 > 5¹¹³ [i]