MinT - Best Known (140−57, 140, s)-Nets in Base 5

Best Known (140−57, 140, s)-Nets in Base 5

(140−57, 140, 252)-Net over F₅ — Constructive and digital

Digital (83, 140, 252)-net over F₅, using

6 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]

(140−57, 140, 283)-Net over F₅ — Digital

Digital (83, 140, 283)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−57, 140, 8313)-Net in Base 5 — Upper bound on s

There is no (83, 140, 8314)-net in base 5, because

1 times m-reduction [i] would yield (83, 139, 8314)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 14 392624 760885 881940 562049 968126 438369 912823 682897 675824 544945 957189 878577 379734 898460 757813 295297 > 5¹³⁹ [i]