MinT - Best Known (194−79, 194, s)-Nets in Base 3

Best Known (194−79, 194, s)-Nets in Base 3

(194−79, 194, 148)-Net over F₃ — Constructive and digital

Digital (115, 194, 148)-net over F₃, using

2 times m-reduction [i] based on digital (115, 196, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 98, 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]

(194−79, 194, 173)-Net over F₃ — Digital

Digital (115, 194, 173)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−79, 194, 1730)-Net in Base 3 — Upper bound on s

There is no (115, 194, 1731)-net in base 3, because

1 times m-reduction [i] would yield (115, 193, 1731)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 124 007535 548655 060805 093299 228417 252351 319378 866026 426059 980593 954171 823788 940926 181686 547651 > 3¹⁹³ [i]