MinT - Best Known (136−53, 136, s)-Nets in Base 5

Best Known (136−53, 136, s)-Nets in Base 5

(136−53, 136, 252)-Net over F₅ — Constructive and digital

Digital (83, 136, 252)-net over F₅, using

10 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]

(136−53, 136, 324)-Net over F₅ — Digital

Digital (83, 136, 324)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−53, 136, 11214)-Net in Base 5 — Upper bound on s

There is no (83, 136, 11215)-net in base 5, because

1 times m-reduction [i] would yield (83, 135, 11215)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 23005 096640 053176 184599 716843 974178 572445 270839 563516 146475 823293 874635 738261 888291 255974 077337 > 5¹³⁵ [i]