MinT - Best Known (241−119, 241, s)-Nets in Base 3

Best Known (241−119, 241, s)-Nets in Base 3

(241−119, 241, 78)-Net over F₃ — Constructive and digital

Digital (122, 241, 78)-net over F₃, using

t-expansion [i] based on digital (121, 241, 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]

(241−119, 241, 122)-Net over F₃ — Digital

Digital (122, 241, 122)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−119, 241, 938)-Net in Base 3 — Upper bound on s

There is no (122, 241, 939)-net in base 3, because

1 times m-reduction [i] would yield (122, 240, 939)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 303271 970470 795353 156526 432076 530813 449659 053290 070033 390662 287547 241515 617032 281912 195249 053959 448721 700710 841947 > 3²⁴⁰ [i]