MinT - Best Known (134, 134+41, s)-Nets in Base 3

Best Known (134, 134+41, s)-Nets in Base 3

(134, 134+41, 464)-Net over F₃ — Constructive and digital

Digital (134, 175, 464)-net over F₃, using

1 times m-reduction [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]

(134, 134+41, 984)-Net over F₃ — Digital

Digital (134, 175, 984)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(134, 134+41, 58760)-Net in Base 3 — Upper bound on s

There is no (134, 175, 58761)-net in base 3, because

1 times m-reduction [i] would yield (134, 174, 58761)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 104505 805160 202825 367466 777197 879905 033052 530325 999085 744336 217659 229679 108374 797649 > 3¹⁷⁴ [i]