MinT - Best Known (83, 132, s)-Nets in Base 3

Best Known (83, 132, s)-Nets in Base 3

(83, 132, 148)-Net over F₃ — Constructive and digital

Digital (83, 132, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 66, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(83, 132, 163)-Net over F₃ — Digital

Digital (83, 132, 163)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 132, 1947)-Net in Base 3 — Upper bound on s

There is no (83, 132, 1948)-net in base 3, because

1 times m-reduction [i] would yield (83, 131, 1948)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 321 012289 693696 437161 186134 899768 530384 478828 926143 088507 060289 > 3¹³¹ [i]