MinT - Best Known (113, 163, s)-Nets in Base 3

Best Known (113, 163, s)-Nets in Base 3

(113, 163, 192)-Net over F₃ — Constructive and digital

Digital (113, 163, 192)-net over F₃, using

3¹ times duplication [i] based on digital (112, 162, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 54, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(113, 163, 346)-Net over F₃ — Digital

Digital (113, 163, 346)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 163, 6543)-Net in Base 3 — Upper bound on s

There is no (113, 163, 6544)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 591148 084525 259566 027651 555636 497588 633682 976537 277133 247223 260701 951173 453345 > 3¹⁶³ [i]