MinT - Best Known (148, 195, s)-Nets in Base 3

Best Known (148, 195, s)-Nets in Base 3

(148, 195, 400)-Net over F₃ — Constructive and digital

Digital (148, 195, 400)-net over F₃, using

1 times m-reduction [i] based on digital (148, 196, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 49, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(148, 195, 965)-Net over F₃ — Digital

Digital (148, 195, 965)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(148, 195, 49847)-Net in Base 3 — Upper bound on s

There is no (148, 195, 49848)-net in base 3, because

1 times m-reduction [i] would yield (148, 194, 49848)-net in base 3, but
- 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]