MinT - Best Known (174−42, 174, s)-Nets in Base 3

Best Known (174−42, 174, s)-Nets in Base 3

(174−42, 174, 400)-Net over F₃ — Constructive and digital

Digital (132, 174, 400)-net over F₃, using

3² times duplication [i] based on digital (130, 172, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 43, 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]

(174−42, 174, 875)-Net over F₃ — Digital

Digital (132, 174, 875)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−42, 174, 38951)-Net in Base 3 — Upper bound on s

There is no (132, 174, 38952)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 104522 195114 039259 974730 874855 526427 962351 705978 369102 822682 832174 610770 253352 257745 > 3¹⁷⁴ [i]