MinT - Best Known (88−39, 88, s)-Nets in Base 3

Best Known (88−39, 88, s)-Nets in Base 3

(88−39, 88, 64)-Net over F₃ — Constructive and digital

Digital (49, 88, 64)-net over F₃, using

trace code for nets [i] based on digital (5, 44, 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]

(88−39, 88, 72)-Net over F₃ — Digital

Digital (49, 88, 72)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−39, 88, 588)-Net in Base 3 — Upper bound on s

There is no (49, 88, 589)-net in base 3, because

1 times m-reduction [i] would yield (49, 87, 589)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 330142 947114 240672 317382 069949 585041 947403 > 3⁸⁷ [i]