MinT - Best Known (99−28, 99, s)-Nets in Base 3

Best Known (99−28, 99, s)-Nets in Base 3

(99−28, 99, 204)-Net over F₃ — Constructive and digital

Digital (71, 99, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 33, 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]

(99−28, 99, 311)-Net over F₃ — Digital

Digital (71, 99, 311)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−28, 99, 7137)-Net in Base 3 — Upper bound on s

There is no (71, 99, 7138)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 172013 494312 273081 040350 219467 973408 350516 117453 > 3⁹⁹ [i]