MinT - Best Known (222−69, 222, s)-Nets in Base 3

Best Known (222−69, 222, s)-Nets in Base 3

(222−69, 222, 204)-Net over F₃ — Constructive and digital

Digital (153, 222, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 74, 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]

(222−69, 222, 435)-Net over F₃ — Digital

Digital (153, 222, 435)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(222−69, 222, 8511)-Net in Base 3 — Upper bound on s

There is no (153, 222, 8512)-net in base 3, because

1 times m-reduction [i] would yield (153, 221, 8512)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2778 656873 419024 095519 864096 393815 069288 144267 893817 594886 701901 402205 352065 751166 263913 017242 302992 471937 > 3²²¹ [i]