MinT - Best Known (106, 106+90, s)-Nets in Base 3

Best Known (106, 106+90, s)-Nets in Base 3

(106, 106+90, 80)-Net over F₃ — Constructive and digital

Digital (106, 196, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 98, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(106, 106+90, 125)-Net over F₃ — Digital

Digital (106, 196, 125)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 106+90, 1011)-Net in Base 3 — Upper bound on s

There is no (106, 196, 1012)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3376 853285 376966 766200 587673 599219 367591 889684 473367 616613 601746 418463 415497 278871 621257 459017 > 3¹⁹⁶ [i]