MinT - Best Known (113, 113+135, s)-Nets in Base 3

Best Known (113, 113+135, s)-Nets in Base 3

(113, 113+135, 74)-Net over F₃ — Constructive and digital

Digital (113, 248, 74)-net over F₃, using

t-expansion [i] based on digital (107, 248, 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+135, 120)-Net over F₃ — Digital

Digital (113, 248, 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+135, 675)-Net in Base 3 — Upper bound on s

There is no (113, 248, 676)-net in base 3, because

1 times m-reduction [i] would yield (113, 247, 676)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7089 131065 007678 916666 581411 535099 314220 423713 913385 375921 234492 979113 011058 556447 304220 400179 068461 265576 015186 211761 > 3²⁴⁷ [i]