MinT - Best Known (135, 135+41, s)-Nets in Base 3

Best Known (135, 135+41, s)-Nets in Base 3

(135, 135+41, 464)-Net over F₃ — Constructive and digital

Digital (135, 176, 464)-net over F₃, using

t-expansion [i] based on digital (134, 176, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 44, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(135, 135+41, 1011)-Net over F₃ — Digital

Digital (135, 176, 1011)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(135, 135+41, 62079)-Net in Base 3 — Upper bound on s

There is no (135, 176, 62080)-net in base 3, because

1 times m-reduction [i] would yield (135, 175, 62080)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 313499 611235 819021 259229 513677 655727 700015 115034 098748 595602 991205 588083 800779 074561 > 3¹⁷⁵ [i]