MinT - Best Known (127−38, 127, s)-Nets in Base 3

Best Known (127−38, 127, s)-Nets in Base 3

(127−38, 127, 192)-Net over F₃ — Constructive and digital

Digital (89, 127, 192)-net over F₃, using

3¹ times duplication [i] based on digital (88, 126, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 42, 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]

(127−38, 127, 306)-Net over F₃ — Digital

Digital (89, 127, 306)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(127−38, 127, 6110)-Net in Base 3 — Upper bound on s

There is no (89, 127, 6111)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 940214 135126 034356 062243 127497 803836 334440 715003 833462 647131 > 3¹²⁷ [i]