MinT - Best Known (230−69, 230, s)-Nets in Base 3

Best Known (230−69, 230, s)-Nets in Base 3

(230−69, 230, 246)-Net over F₃ — Constructive and digital

Digital (161, 230, 246)-net over F₃, using

1 times m-reduction [i] based on digital (161, 231, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 77, 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]

(230−69, 230, 501)-Net over F₃ — Digital

Digital (161, 230, 501)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−69, 230, 11032)-Net in Base 3 — Upper bound on s

There is no (161, 230, 11033)-net in base 3, because

1 times m-reduction [i] would yield (161, 229, 11033)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 245199 528519 348778 307884 194907 831443 408218 263688 018501 021316 516599 436220 539972 007697 945141 032180 564811 763705 > 3²²⁹ [i]