MinT - Best Known (163−37, 163, s)-Nets in Base 3

Best Known (163−37, 163, s)-Nets in Base 3

(163−37, 163, 464)-Net over F₃ — Constructive and digital

Digital (126, 163, 464)-net over F₃, using

t-expansion [i] based on digital (125, 163, 464)-net over F₃, using
- 1 times m-reduction [i] based on digital (125, 164, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 41, 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]

(163−37, 163, 1050)-Net over F₃ — Digital

Digital (126, 163, 1050)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−37, 163, 74317)-Net in Base 3 — Upper bound on s

There is no (126, 163, 74318)-net in base 3, because

1 times m-reduction [i] would yield (126, 162, 74318)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 196667 014697 274508 485998 233637 570007 631553 384960 607527 773680 217285 407650 932605 > 3¹⁶² [i]