MinT - Best Known (106, 106+72, s)-Nets in Base 3

Best Known (106, 106+72, s)-Nets in Base 3

(106, 106+72, 148)-Net over F₃ — Constructive and digital

Digital (106, 178, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 89, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(106, 106+72, 164)-Net over F₃ — Digital

Digital (106, 178, 164)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 106+72, 1597)-Net in Base 3 — Upper bound on s

There is no (106, 178, 1598)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 625528 786033 050180 285273 036895 057653 378622 695156 130745 394395 663647 168500 475824 149833 > 3¹⁷⁸ [i]