MinT - Best Known (101, 101+51, s)-Nets in Base 3

Best Known (101, 101+51, s)-Nets in Base 3

(101, 101+51, 156)-Net over F₃ — Constructive and digital

Digital (101, 152, 156)-net over F₃, using

6 times m-reduction [i] based on digital (101, 158, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 79, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(101, 101+51, 248)-Net over F₃ — Digital

Digital (101, 152, 248)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 101+51, 3851)-Net in Base 3 — Upper bound on s

There is no (101, 152, 3852)-net in base 3, because

1 times m-reduction [i] would yield (101, 151, 3852)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 111522 362681 947091 611800 612379 054314 779717 240253 074766 851688 772952 461721 > 3¹⁵¹ [i]