MinT - Best Known (75, 105, s)-Nets in Base 3

Best Known (75, 105, s)-Nets in Base 3

(75, 105, 204)-Net over F₃ — Constructive and digital

Digital (75, 105, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 35, 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]

(75, 105, 312)-Net over F₃ — Digital

Digital (75, 105, 312)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 105, 7009)-Net in Base 3 — Upper bound on s

There is no (75, 105, 7010)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 125 363168 521455 417223 644328 981813 415095 262127 014681 > 3¹⁰⁵ [i]