MinT - Best Known (207−58, 207, s)-Nets in Base 3

Best Known (207−58, 207, s)-Nets in Base 3

(207−58, 207, 288)-Net over F₃ — Constructive and digital

Digital (149, 207, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 69, 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]

(207−58, 207, 573)-Net over F₃ — Digital

Digital (149, 207, 573)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−58, 207, 14822)-Net in Base 3 — Upper bound on s

There is no (149, 207, 14823)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 581 635568 383512 510558 270762 520405 657649 407502 197493 421301 850228 605358 680931 403125 586009 178232 323543 > 3²⁰⁷ [i]