MinT - Best Known (113, 113+115, s)-Nets in Base 3

Best Known (113, 113+115, s)-Nets in Base 3

(113, 113+115, 74)-Net over F₃ — Constructive and digital

Digital (113, 228, 74)-net over F₃, using

t-expansion [i] based on digital (107, 228, 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]

(113, 113+115, 120)-Net over F₃ — Digital

Digital (113, 228, 120)-net over F₃, using

net from sequence [i] based on digital (113, 119)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 113 and N(F) ≥ 120, using
  - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(113, 113+115, 822)-Net in Base 3 — Upper bound on s

There is no (113, 228, 823)-net in base 3, because

1 times m-reduction [i] would yield (113, 227, 823)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 143740 456205 064714 542636 330251 181722 778355 103698 098056 571647 479075 941629 353427 238719 645462 757670 481355 855359 > 3²²⁷ [i]