MinT - Best Known (135−37, 135, s)-Nets in Base 3

Best Known (135−37, 135, s)-Nets in Base 3

(135−37, 135, 252)-Net over F₃ — Constructive and digital

Digital (98, 135, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 45, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(135−37, 135, 438)-Net over F₃ — Digital

Digital (98, 135, 438)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−37, 135, 13441)-Net in Base 3 — Upper bound on s

There is no (98, 135, 13442)-net in base 3, because

1 times m-reduction [i] would yield (98, 134, 13442)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8604 270509 443854 958375 821035 945273 128460 896660 018252 848796 426165 > 3¹³⁴ [i]