MinT - Best Known (130−54, 130, s)-Nets in Base 3

Best Known (130−54, 130, s)-Nets in Base 3

(130−54, 130, 80)-Net over F₃ — Constructive and digital

Digital (76, 130, 80)-net over F₃, using

6 times m-reduction [i] based on digital (76, 136, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 68, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(130−54, 130, 117)-Net over F₃ — Digital

Digital (76, 130, 117)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−54, 130, 1056)-Net in Base 3 — Upper bound on s

There is no (76, 130, 1057)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 106 736727 499506 927428 542781 141794 063869 514690 603875 380464 876347 > 3¹³⁰ [i]