MinT - Best Known (67, 67+37, s)-Nets in Base 5

Best Known (67, 67+37, s)-Nets in Base 5

(67, 67+37, 252)-Net over F₅ — Constructive and digital

Digital (67, 104, 252)-net over F₅, using

10 times m-reduction [i] based on digital (67, 114, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 57, 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]

(67, 67+37, 375)-Net over F₅ — Digital

Digital (67, 104, 375)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+37, 18855)-Net in Base 5 — Upper bound on s

There is no (67, 104, 18856)-net in base 5, because

1 times m-reduction [i] would yield (67, 103, 18856)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 986773 321689 921180 987141 854683 338131 344029 256460 249854 767091 832711 761025 > 5¹⁰³ [i]