MinT - Best Known (194−45, 194, s)-Nets in Base 3

Best Known (194−45, 194, s)-Nets in Base 3

(194−45, 194, 464)-Net over F₃ — Constructive and digital

Digital (149, 194, 464)-net over F₃, using

2 times m-reduction [i] based on digital (149, 196, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 49, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(194−45, 194, 1117)-Net over F₃ — Digital

Digital (149, 194, 1117)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−45, 194, 69397)-Net in Base 3 — Upper bound on s

There is no (149, 194, 69398)-net in base 3, because

1 times m-reduction [i] would yield (149, 193, 69398)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 121 474611 145051 922727 751881 334418 348642 456472 232097 512616 647545 451062 081576 139608 338645 541717 > 3¹⁹³ [i]