MinT - Best Known (107, 107+72, s)-Nets in Base 3

Best Known (107, 107+72, s)-Nets in Base 3

(107, 107+72, 148)-Net over F₃ — Constructive and digital

Digital (107, 179, 148)-net over F₃, using

1 times m-reduction [i] based on digital (107, 180, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 90, 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]

(107, 107+72, 167)-Net over F₃ — Digital

Digital (107, 179, 167)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 107+72, 1647)-Net in Base 3 — Upper bound on s

There is no (107, 179, 1648)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25 547385 158587 468618 360689 584690 969219 737872 767452 981084 971545 130181 011590 058138 788481 > 3¹⁷⁹ [i]