MinT - Best Known (163−46, 163, s)-Nets in Base 3

Best Known (163−46, 163, s)-Nets in Base 3

(163−46, 163, 252)-Net over F₃ — Constructive and digital

Digital (117, 163, 252)-net over F₃, using

3¹ times duplication [i] based on digital (116, 162, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 54, 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]

(163−46, 163, 458)-Net over F₃ — Digital

Digital (117, 163, 458)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−46, 163, 11321)-Net in Base 3 — Upper bound on s

There is no (117, 163, 11322)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 590530 485475 979544 955856 732904 756866 905664 513701 421428 693340 259608 195206 298601 > 3¹⁶³ [i]