MinT - Best Known (165−46, 165, s)-Nets in Base 3

Best Known (165−46, 165, s)-Nets in Base 3

(165−46, 165, 264)-Net over F₃ — Constructive and digital

Digital (119, 165, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 55, 88)-net over F₂₇, using
- net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
    - a function field by SÃ©mirat [i]

(165−46, 165, 483)-Net over F₃ — Digital

Digital (119, 165, 483)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(165−46, 165, 12458)-Net in Base 3 — Upper bound on s

There is no (119, 165, 12459)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5 312731 565040 973997 417661 392797 087209 138015 085482 110070 778771 255692 911263 560195 > 3¹⁶⁵ [i]