MinT - Best Known (102−37, 102, s)-Nets in Base 5

Best Known (102−37, 102, s)-Nets in Base 5

(102−37, 102, 252)-Net over F₅ — Constructive and digital

Digital (65, 102, 252)-net over F₅, using

8 times m-reduction [i] based on digital (65, 110, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 55, 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]

(102−37, 102, 341)-Net over F₅ — Digital

Digital (65, 102, 341)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(102−37, 102, 15765)-Net in Base 5 — Upper bound on s

There is no (65, 102, 15766)-net in base 5, because

1 times m-reduction [i] would yield (65, 101, 15766)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 39460 944119 580700 773514 837463 199123 165386 338558 516938 272159 134364 682625 > 5¹⁰¹ [i]