MinT - Best Known (178−42, 178, s)-Nets in Base 3

Best Known (178−42, 178, s)-Nets in Base 3

(178−42, 178, 464)-Net over F₃ — Constructive and digital

Digital (136, 178, 464)-net over F₃, using

3² times duplication [i] based on digital (134, 176, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 44, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(178−42, 178, 971)-Net over F₃ — Digital

Digital (136, 178, 971)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−42, 178, 48022)-Net in Base 3 — Upper bound on s

There is no (136, 178, 48023)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 464722 235653 090028 263957 924905 883816 585318 321033 164032 646506 509117 377389 563381 106887 > 3¹⁷⁸ [i]