MinT - Best Known (111−33, 111, s)-Nets in Base 5

Best Known (111−33, 111, s)-Nets in Base 5

(111−33, 111, 296)-Net over F₅ — Constructive and digital

Digital (78, 111, 296)-net over F₅, using

7 times m-reduction [i] based on digital (78, 118, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 59, 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]

(111−33, 111, 866)-Net over F₅ — Digital

Digital (78, 111, 866)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(111−33, 111, 108605)-Net in Base 5 — Upper bound on s

There is no (78, 111, 108606)-net in base 5, because

1 times m-reduction [i] would yield (78, 110, 108606)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 77043 691029 206568 747271 634176 265742 925276 918090 839604 790931 897094 728656 455425 > 5¹¹⁰ [i]