MinT - Best Known (113, 113+40, s)-Nets in Base 3

Best Known (113, 113+40, s)-Nets in Base 3

(113, 113+40, 288)-Net over F₃ — Constructive and digital

Digital (113, 153, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 51, 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]

(113, 113+40, 577)-Net over F₃ — Digital

Digital (113, 153, 577)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 113+40, 18526)-Net in Base 3 — Upper bound on s

There is no (113, 153, 18527)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9 993337 568417 665996 982456 067171 617414 333855 243331 230188 677163 206083 481561 > 3¹⁵³ [i]