MinT - Best Known (241−59, 241, s)-Nets in Base 3

Best Known (241−59, 241, s)-Nets in Base 3

(241−59, 241, 400)-Net over F₃ — Constructive and digital

Digital (182, 241, 400)-net over F₃, using

3¹ times duplication [i] based on digital (181, 240, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 60, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(241−59, 241, 1077)-Net over F₃ — Digital

Digital (182, 241, 1077)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−59, 241, 51813)-Net in Base 3 — Upper bound on s

There is no (182, 241, 51814)-net in base 3, because

1 times m-reduction [i] would yield (182, 240, 51814)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 230142 021046 105420 916719 702782 641944 050823 042241 410221 305904 435923 648333 628764 192808 517569 896383 864985 347307 053941 > 3²⁴⁰ [i]