MinT - Best Known (130−35, 130, s)-Nets in Base 3

Best Known (130−35, 130, s)-Nets in Base 3

(130−35, 130, 252)-Net over F₃ — Constructive and digital

Digital (95, 130, 252)-net over F₃, using

3¹ times duplication [i] based on digital (94, 129, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 43, 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]

(130−35, 130, 455)-Net over F₃ — Digital

Digital (95, 130, 455)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−35, 130, 14960)-Net in Base 3 — Upper bound on s

There is no (95, 130, 14961)-net in base 3, because

1 times m-reduction [i] would yield (95, 129, 14961)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 35 392092 622560 450837 297930 776782 684038 161031 359798 190660 095139 > 3¹²⁹ [i]