MinT - Best Known (83, 83+31, s)-Nets in Base 3

Best Known (83, 83+31, s)-Nets in Base 3

(83, 83+31, 246)-Net over F₃ — Constructive and digital

Digital (83, 114, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 38, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(83, 83+31, 398)-Net over F₃ — Digital

Digital (83, 114, 398)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 83+31, 12605)-Net in Base 3 — Upper bound on s

There is no (83, 114, 12606)-net in base 3, because

1 times m-reduction [i] would yield (83, 113, 12606)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 822422 798372 069720 160121 451330 564100 495973 627003 048041 > 3¹¹³ [i]