MinT - Best Known (123, 123+116, s)-Nets in Base 3

Best Known (123, 123+116, s)-Nets in Base 3

(123, 123+116, 78)-Net over F₃ — Constructive and digital

Digital (123, 239, 78)-net over F₃, using

t-expansion [i] based on digital (121, 239, 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]

(123, 123+116, 127)-Net over F₃ — Digital

Digital (123, 239, 127)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 123+116, 981)-Net in Base 3 — Upper bound on s

There is no (123, 239, 982)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 079318 302707 611328 892988 779056 570075 965891 118690 605169 007559 453238 051222 640522 135354 264127 081636 973529 151799 058365 > 3²³⁹ [i]