MinT - Best Known (138−53, 138, s)-Nets in Base 5

Best Known (138−53, 138, s)-Nets in Base 5

(138−53, 138, 252)-Net over F₅ — Constructive and digital

Digital (85, 138, 252)-net over F₅, using

12 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]

(138−53, 138, 346)-Net over F₅ — Digital

Digital (85, 138, 346)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−53, 138, 12694)-Net in Base 5 — Upper bound on s

There is no (85, 138, 12695)-net in base 5, because

1 times m-reduction [i] would yield (85, 137, 12695)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 574472 282770 668494 538576 214140 608020 226125 079714 727179 982260 939439 816558 749215 783427 196981 963673 > 5¹³⁷ [i]