MinT - Best Known (86, 86+32, s)-Nets in Base 3

Best Known (86, 86+32, s)-Nets in Base 3

(86, 86+32, 246)-Net over F₃ — Constructive and digital

Digital (86, 118, 246)-net over F₃, using

3¹ times duplication [i] based on digital (85, 117, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 39, 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]

(86, 86+32, 412)-Net over F₃ — Digital

Digital (86, 118, 412)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+32, 11211)-Net in Base 3 — Upper bound on s

There is no (86, 118, 11212)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 199 702643 568781 327379 720402 797458 054571 722219 306729 586305 > 3¹¹⁸ [i]