MinT - Best Known (136−51, 136, s)-Nets in Base 5

Best Known (136−51, 136, s)-Nets in Base 5

(136−51, 136, 252)-Net over F₅ — Constructive and digital

Digital (85, 136, 252)-net over F₅, using

14 times m-reduction [i] based on digital (85, 150, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 75, 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]

(136−51, 136, 375)-Net over F₅ — Digital

Digital (85, 136, 375)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−51, 136, 15117)-Net in Base 5 — Upper bound on s

There is no (85, 136, 15118)-net in base 5, because

1 times m-reduction [i] would yield (85, 135, 15118)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 22977 656769 044056 219353 267645 441730 311603 987099 369255 469701 801069 177897 568211 536093 803208 108601 > 5¹³⁵ [i]