MinT - Best Known (129−35, 129, s)-Nets in Base 3

Best Known (129−35, 129, s)-Nets in Base 3

(129−35, 129, 252)-Net over F₃ — Constructive and digital

Digital (94, 129, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 43, 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]

(129−35, 129, 439)-Net over F₃ — Digital

Digital (94, 129, 439)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−35, 129, 14023)-Net in Base 3 — Upper bound on s

There is no (94, 129, 14024)-net in base 3, because

1 times m-reduction [i] would yield (94, 128, 14024)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 801600 246374 280551 825650 014014 552140 309094 514863 251664 574097 > 3¹²⁸ [i]