MinT - Best Known (194−46, 194, s)-Nets in Base 3

Best Known (194−46, 194, s)-Nets in Base 3

(194−46, 194, 464)-Net over F₃ — Constructive and digital

Digital (148, 194, 464)-net over F₃, using

3² times duplication [i] based on digital (146, 192, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 48, 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]

(194−46, 194, 1027)-Net over F₃ — Digital

Digital (148, 194, 1027)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−46, 194, 49847)-Net in Base 3 — Upper bound on s

There is no (148, 194, 49848)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 364 418350 681415 049009 582692 974017 231869 068652 770238 190235 711321 149142 589907 352144 756938 853281 > 3¹⁹⁴ [i]