MinT - Best Known (99, 135, s)-Nets in Base 3

Best Known (99, 135, s)-Nets in Base 3

(99, 135, 264)-Net over F₃ — Constructive and digital

Digital (99, 135, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 45, 88)-net over F₂₇, using
- net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
    - a function field by SÃ©mirat [i]

(99, 135, 486)-Net over F₃ — Digital

Digital (99, 135, 486)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 135, 14288)-Net in Base 3 — Upper bound on s

There is no (99, 135, 14289)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25810 427256 082960 272462 949662 785370 737430 579983 813661 727635 475305 > 3¹³⁵ [i]