MinT - Best Known (77, 77+33, s)-Nets in Base 5

Best Known (77, 77+33, s)-Nets in Base 5

(77, 77+33, 296)-Net over F₅ — Constructive and digital

Digital (77, 110, 296)-net over F₅, using

6 times m-reduction [i] based on digital (77, 116, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 58, 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]

(77, 77+33, 824)-Net over F₅ — Digital

Digital (77, 110, 824)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+33, 98211)-Net in Base 5 — Upper bound on s

There is no (77, 110, 98212)-net in base 5, because

1 times m-reduction [i] would yield (77, 109, 98212)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 15409 435081 689943 228692 777734 519176 841019 372492 345743 519553 703973 793434 415105 > 5¹⁰⁹ [i]