MinT - Best Known (142−53, 142, s)-Nets in Base 5

Best Known (142−53, 142, s)-Nets in Base 5

(142−53, 142, 252)-Net over F₅ — Constructive and digital

Digital (89, 142, 252)-net over F₅, using

t-expansion [i] based on 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]

(142−53, 142, 396)-Net over F₅ — Digital

Digital (89, 142, 396)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−53, 142, 16266)-Net in Base 5 — Upper bound on s

There is no (89, 142, 16267)-net in base 5, because

1 times m-reduction [i] would yield (89, 141, 16267)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 359 013204 040397 101997 009885 155638 104706 629275 984576 195414 259507 657679 133687 473001 212024 844821 984025 > 5¹⁴¹ [i]