MinT - Best Known (205−61, 205, s)-Nets in Base 3

Best Known (205−61, 205, s)-Nets in Base 3

(205−61, 205, 246)-Net over F₃ — Constructive and digital

Digital (144, 205, 246)-net over F₃, using

3¹ times duplication [i] based on digital (143, 204, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 68, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(205−61, 205, 465)-Net over F₃ — Digital

Digital (144, 205, 465)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−61, 205, 10543)-Net in Base 3 — Upper bound on s

There is no (144, 205, 10544)-net in base 3, because

1 times m-reduction [i] would yield (144, 204, 10544)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21 565551 282895 628141 557397 522071 262070 839642 432678 644953 240104 183291 542436 788881 148290 685290 796065 > 3²⁰⁴ [i]