MinT - Best Known (122, 122+115, s)-Nets in Base 3

Best Known (122, 122+115, s)-Nets in Base 3

(122, 122+115, 78)-Net over F₃ — Constructive and digital

Digital (122, 237, 78)-net over F₃, using

t-expansion [i] based on digital (121, 237, 78)-net over F₃, using
- net from sequence [i] based on digital (121, 77)-sequence over F₃, using
  - base reduction for sequences [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]

(122, 122+115, 126)-Net over F₃ — Digital

Digital (122, 237, 126)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(122, 122+115, 988)-Net in Base 3 — Upper bound on s

There is no (122, 237, 989)-net in base 3, because

1 times m-reduction [i] would yield (122, 236, 989)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 41986 952602 465316 169570 972052 114164 527377 867979 674818 454884 934932 760361 206611 797537 671152 669203 237374 025554 621659 > 3²³⁶ [i]