MinT - Best Known (213−60, 213, s)-Nets in Base 3

Best Known (213−60, 213, s)-Nets in Base 3

(213−60, 213, 288)-Net over F₃ — Constructive and digital

Digital (153, 213, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 71, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(213−60, 213, 576)-Net over F₃ — Digital

Digital (153, 213, 576)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(213−60, 213, 14670)-Net in Base 3 — Upper bound on s

There is no (153, 213, 14671)-net in base 3, because

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]