MinT - Best Known (157−44, 157, s)-Nets in Base 3

Best Known (157−44, 157, s)-Nets in Base 3

(157−44, 157, 252)-Net over F₃ — Constructive and digital

Digital (113, 157, 252)-net over F₃, using

3¹ times duplication [i] based on digital (112, 156, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 52, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(157−44, 157, 455)-Net over F₃ — Digital

Digital (113, 157, 455)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−44, 157, 11479)-Net in Base 3 — Upper bound on s

There is no (113, 157, 11480)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 809 986914 137832 473985 067461 868542 258844 037994 380374 860853 791924 889703 317521 > 3¹⁵⁷ [i]