MinT - Best Known (113, 113+121, s)-Nets in Base 3

Best Known (113, 113+121, s)-Nets in Base 3

(113, 113+121, 74)-Net over F₃ — Constructive and digital

Digital (113, 234, 74)-net over F₃, using

t-expansion [i] based on digital (107, 234, 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+121, 120)-Net over F₃ — Digital

Digital (113, 234, 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+121, 768)-Net in Base 3 — Upper bound on s

There is no (113, 234, 769)-net in base 3, because

1 times m-reduction [i] would yield (113, 233, 769)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1531 513569 006146 223017 505625 926931 498078 316213 748196 498822 988490 194297 244929 899315 476299 832556 043219 074767 089073 > 3²³³ [i]