MinT - Best Known (83, 83+61, s)-Nets in Base 5

Best Known (83, 83+61, s)-Nets in Base 5

(83, 83+61, 252)-Net over F₅ — Constructive and digital

Digital (83, 144, 252)-net over F₅, using

2 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]

(83, 83+61, 6441)-Net in Base 5 — Upper bound on s

There is no (83, 144, 6442)-net in base 5, because

1 times m-reduction [i] would yield (83, 143, 6442)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 8976 894494 383819 430285 502883 389905 335989 760044 819646 689950 335575 330844 507732 617386 438190 826848 892161 > 5¹⁴³ [i]