MinT - Best Known (62, 62+52, s)-Nets in Base 3

Best Known (62, 62+52, s)-Nets in Base 3

(62, 62+52, 64)-Net over F₃ — Constructive and digital

Digital (62, 114, 64)-net over F₃, using

trace code for nets [i] based on digital (5, 57, 32)-net over F₉, using
- net from sequence [i] based on digital (5, 31)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
    - a function field by GarcÃa and Quoos [i]

(62, 62+52, 81)-Net over F₃ — Digital

Digital (62, 114, 81)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+52, 626)-Net in Base 3 — Upper bound on s

There is no (62, 114, 627)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 472806 084394 206393 433078 518367 050446 579940 303442 313365 > 3¹¹⁴ [i]