MinT - Best Known (68, 68+28, s)-Nets in Base 3

Best Known (68, 68+28, s)-Nets in Base 3

(68, 68+28, 192)-Net over F₃ — Constructive and digital

Digital (68, 96, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 32, 64)-net over F₂₇, using
- net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(68, 68+28, 272)-Net over F₃ — Digital

Digital (68, 96, 272)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+28, 5637)-Net in Base 3 — Upper bound on s

There is no (68, 96, 5638)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6372 198757 783545 290385 148203 636179 809194 266853 > 3⁹⁶ [i]