MinT - Best Known (141, 141+61, s)-Nets in Base 3

Best Known (141, 141+61, s)-Nets in Base 3

(141, 141+61, 228)-Net over F₃ — Constructive and digital

Digital (141, 202, 228)-net over F₃, using

3¹ times duplication [i] based on digital (140, 201, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 67, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(141, 141+61, 438)-Net over F₃ — Digital

Digital (141, 202, 438)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(141, 141+61, 9443)-Net in Base 3 — Upper bound on s

There is no (141, 202, 9444)-net in base 3, because

1 times m-reduction [i] would yield (141, 201, 9444)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 798915 543632 046778 029515 985634 920160 684204 508898 985947 095451 258543 886609 328822 359109 023275 496473 > 3²⁰¹ [i]