MinT - Best Known (101, 101+83, s)-Nets in Base 3

Best Known (101, 101+83, s)-Nets in Base 3

(101, 101+83, 80)-Net over F₃ — Constructive and digital

Digital (101, 184, 80)-net over F₃, using

2 times m-reduction [i] based on digital (101, 186, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 93, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(101, 101+83, 124)-Net over F₃ — Digital

Digital (101, 184, 124)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 101+83, 1047)-Net in Base 3 — Upper bound on s

There is no (101, 184, 1048)-net in base 3, because

1 times m-reduction [i] would yield (101, 183, 1048)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2078 149515 411688 166716 971669 050717 646358 507035 179081 127016 924222 125707 523713 090822 235825 > 3¹⁸³ [i]