MinT - Best Known (90, 90+34, s)-Nets in Base 3

Best Known (90, 90+34, s)-Nets in Base 3

(90, 90+34, 246)-Net over F₃ — Constructive and digital

Digital (90, 124, 246)-net over F₃, using

3¹ times duplication [i] based on digital (89, 123, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 41, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(90, 90+34, 410)-Net over F₃ — Digital

Digital (90, 124, 410)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+34, 10825)-Net in Base 3 — Upper bound on s

There is no (90, 124, 10826)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 145758 731981 912171 621523 660228 282568 316509 267779 564111 820533 > 3¹²⁴ [i]