MinT - Best Known (203−83, 203, s)-Nets in Base 3

Best Known (203−83, 203, s)-Nets in Base 3

(203−83, 203, 148)-Net over F₃ — Constructive and digital

Digital (120, 203, 148)-net over F₃, using

3 times m-reduction [i] based on digital (120, 206, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 103, 74)-net over F₉, using
  - net from sequence [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]

(203−83, 203, 178)-Net over F₃ — Digital

Digital (120, 203, 178)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(203−83, 203, 1769)-Net in Base 3 — Upper bound on s

There is no (120, 203, 1770)-net in base 3, because

1 times m-reduction [i] would yield (120, 202, 1770)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 420278 766286 217276 938092 319219 284751 334094 691264 662125 830077 424812 294299 597574 155310 309010 219205 > 3²⁰² [i]