MinT - Best Known (236−121, 236, s)-Nets in Base 3

Best Known (236−121, 236, s)-Nets in Base 3

(236−121, 236, 74)-Net over F₃ — Constructive and digital

Digital (115, 236, 74)-net over F₃, using

t-expansion [i] based on digital (107, 236, 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]

(236−121, 236, 120)-Net over F₃ — Digital

Digital (115, 236, 120)-net over F₃, using

t-expansion [i] based on digital (113, 236, 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]

(236−121, 236, 799)-Net in Base 3 — Upper bound on s

There is no (115, 236, 800)-net in base 3, because

1 times m-reduction [i] would yield (115, 235, 800)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13998 877307 438533 222176 028328 207624 553190 817390 682581 316342 868649 050448 067599 922653 550803 935025 517903 790685 940481 > 3²³⁵ [i]