MinT - Best Known (201−62, 201, s)-Nets in Base 3

Best Known (201−62, 201, s)-Nets in Base 3

(201−62, 201, 204)-Net over F₃ — Constructive and digital

Digital (139, 201, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 67, 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]

(201−62, 201, 408)-Net over F₃ — Digital

Digital (139, 201, 408)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(201−62, 201, 7671)-Net in Base 3 — Upper bound on s

There is no (139, 201, 7672)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 798735 511343 702657 919011 731143 106551 380954 726850 499527 266976 971096 155666 877706 789055 210774 469025 > 3²⁰¹ [i]