MinT - Best Known (76−27, 76, s)-Nets in Base 5

Best Known (76−27, 76, s)-Nets in Base 5

(76−27, 76, 252)-Net over F₅ — Constructive and digital

Digital (49, 76, 252)-net over F₅, using

2 times m-reduction [i] based on digital (49, 78, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 39, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(76−27, 76, 303)-Net over F₅ — Digital

Digital (49, 76, 303)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(76−27, 76, 15261)-Net in Base 5 — Upper bound on s

There is no (49, 76, 15262)-net in base 5, because

1 times m-reduction [i] would yield (49, 75, 15262)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 26476 979613 080300 855633 102276 783942 976052 773728 114425 > 5⁷⁵ [i]