MinT - Best Known (153, 153+61, s)-Nets in Base 3

Best Known (153, 153+61, s)-Nets in Base 3

(153, 153+61, 282)-Net over F₃ — Constructive and digital

Digital (153, 214, 282)-net over F₃, using

3¹ times duplication [i] based on digital (152, 213, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 71, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(153, 153+61, 556)-Net over F₃ — Digital

Digital (153, 214, 556)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(153, 153+61, 14670)-Net in Base 3 — Upper bound on s

There is no (153, 214, 14671)-net in base 3, because

1 times m-reduction [i] would yield (153, 213, 14671)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 423819 646228 496998 107615 504992 082577 818181 385249 744732 131624 931168 118725 281364 983436 858319 328527 055845 > 3²¹³ [i]