MinT - Best Known (166−50, 166, s)-Nets in Base 4

Best Known (166−50, 166, s)-Nets in Base 4

(166−50, 166, 384)-Net over F₄ — Constructive and digital

Digital (116, 166, 384)-net over F₄, using

4¹ times duplication [i] based on digital (115, 165, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 55, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(166−50, 166, 699)-Net over F₄ — Digital

Digital (116, 166, 699)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−50, 166, 33722)-Net in Base 4 — Upper bound on s

There is no (116, 166, 33723)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8751 524713 199100 131640 392901 438873 904146 304102 205938 906360 943449 398755 500098 577468 174704 123046 322758 > 4¹⁶⁶ [i]