MinT - Best Known (59, 59+49, s)-Nets in Base 3

Best Known (59, 59+49, s)-Nets in Base 3

(59, 59+49, 64)-Net over F₃ — Constructive and digital

Digital (59, 108, 64)-net over F₃, using

trace code for nets [i] based on digital (5, 54, 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]

(59, 59+49, 79)-Net over F₃ — Digital

Digital (59, 108, 79)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+49, 633)-Net in Base 3 — Upper bound on s

There is no (59, 108, 634)-net in base 3, because

1 times m-reduction [i] would yield (59, 107, 634)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1137 751312 733003 197414 484485 395296 684785 267638 938481 > 3¹⁰⁷ [i]