MinT - Best Known (142−57, 142, s)-Nets in Base 5

Best Known (142−57, 142, s)-Nets in Base 5

(142−57, 142, 252)-Net over F₅ — Constructive and digital

Digital (85, 142, 252)-net over F₅, using

8 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]

(142−57, 142, 301)-Net over F₅ — Digital

Digital (85, 142, 301)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−57, 142, 9328)-Net in Base 5 — Upper bound on s

There is no (85, 142, 9329)-net in base 5, because

1 times m-reduction [i] would yield (85, 141, 9329)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 359 412181 899257 023145 002456 905693 684194 002088 843152 295975 732755 773169 672911 459041 760980 923519 077393 > 5¹⁴¹ [i]