MinT - Best Known (127, 127+66, s)-Nets in Base 3

Best Known (127, 127+66, s)-Nets in Base 3

(127, 127+66, 156)-Net over F₃ — Constructive and digital

Digital (127, 193, 156)-net over F₃, using

17 times m-reduction [i] based on digital (127, 210, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 105, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(127, 127+66, 285)-Net over F₃ — Digital

Digital (127, 193, 285)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 127+66, 4029)-Net in Base 3 — Upper bound on s

There is no (127, 193, 4030)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 121 647723 396694 665051 965439 799580 193319 856083 876726 173681 303410 111243 472769 593579 015445 104445 > 3¹⁹³ [i]