MinT - Best Known (72−27, 72, s)-Nets in Base 5

Best Known (72−27, 72, s)-Nets in Base 5

(72−27, 72, 208)-Net over F₅ — Constructive and digital

Digital (45, 72, 208)-net over F₅, using

trace code for nets [i] based on digital (9, 36, 104)-net over F₂₅, using
- net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
    - a function field by GarcÃa and Quoos [i]

(72−27, 72, 231)-Net over F₅ — Digital

Digital (45, 72, 231)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(72−27, 72, 9297)-Net in Base 5 — Upper bound on s

There is no (45, 72, 9298)-net in base 5, because

1 times m-reduction [i] would yield (45, 71, 9298)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 42 381415 844969 726104 764887 927410 835939 895947 900745 > 5⁷¹ [i]