MinT - Best Known (138−55, 138, s)-Nets in Base 5

Best Known (138−55, 138, s)-Nets in Base 5

(138−55, 138, 252)-Net over F₅ — Constructive and digital

Digital (83, 138, 252)-net over F₅, using

8 times m-reduction [i] based on digital (83, 146, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 73, 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]

(138−55, 138, 302)-Net over F₅ — Digital

Digital (83, 138, 302)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−55, 138, 9595)-Net in Base 5 — Upper bound on s

There is no (83, 138, 9596)-net in base 5, because

1 times m-reduction [i] would yield (83, 137, 9596)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 574334 165921 897138 614121 812425 090370 572018 800519 484852 608168 231775 819384 793621 870841 285982 193905 > 5¹³⁷ [i]