MinT - Best Known (88, 88+32, s)-Nets in Base 3

Best Known (88, 88+32, s)-Nets in Base 3

(88, 88+32, 252)-Net over F₃ — Constructive and digital

Digital (88, 120, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 40, 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]

(88, 88+32, 445)-Net over F₃ — Digital

Digital (88, 120, 445)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+32, 12864)-Net in Base 3 — Upper bound on s

There is no (88, 120, 12865)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1797 958554 270644 513886 387138 624352 510051 825405 397287 135041 > 3¹²⁰ [i]