MinT - Best Known (88, 88+36, s)-Nets in Base 3

Best Known (88, 88+36, s)-Nets in Base 3

(88, 88+36, 204)-Net over F₃ — Constructive and digital

Digital (88, 124, 204)-net over F₃, using

3¹ times duplication [i] based on digital (87, 123, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 41, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(88, 88+36, 333)-Net over F₃ — Digital

Digital (88, 124, 333)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+36, 7292)-Net in Base 3 — Upper bound on s

There is no (88, 124, 7293)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 145622 217048 819189 629125 188312 336681 495863 619083 708194 746945 > 3¹²⁴ [i]