MinT - Best Known (241−75, 241, s)-Nets in Base 3

Best Known (241−75, 241, s)-Nets in Base 3

(241−75, 241, 204)-Net over F₃ — Constructive and digital

Digital (166, 241, 204)-net over F₃, using

3¹ times duplication [i] based on digital (165, 240, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 80, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(241−75, 241, 465)-Net over F₃ — Digital

Digital (166, 241, 465)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−75, 241, 9077)-Net in Base 3 — Upper bound on s

There is no (166, 241, 9078)-net in base 3, because

1 times m-reduction [i] would yield (166, 240, 9078)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 231327 612823 498705 982659 452741 126843 048927 608269 987801 904092 404062 468277 452911 699561 408852 364887 987099 435555 197957 > 3²⁴⁰ [i]