MinT - Best Known (226−115, 226, s)-Nets in Base 3

Best Known (226−115, 226, s)-Nets in Base 3

(226−115, 226, 74)-Net over F₃ — Constructive and digital

Digital (111, 226, 74)-net over F₃, using

t-expansion [i] based on digital (107, 226, 74)-net over F₃, using
- net from sequence [i] based on digital (107, 73)-sequence over F₃, using
  - base reduction for sequences [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(226−115, 226, 106)-Net over F₃ — Digital

Digital (111, 226, 106)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−115, 226, 789)-Net in Base 3 — Upper bound on s

There is no (111, 226, 790)-net in base 3, because

1 times m-reduction [i] would yield (111, 225, 790)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 240568 756531 682779 009115 663734 904373 864207 974154 085284 529681 224141 500919 952850 777375 242782 159747 179106 767677 > 3²²⁵ [i]