MinT - Best Known (101−29, 101, s)-Nets in Base 3

Best Known (101−29, 101, s)-Nets in Base 3

(101−29, 101, 192)-Net over F₃ — Constructive and digital

Digital (72, 101, 192)-net over F₃, using

1 times m-reduction [i] based on digital (72, 102, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 34, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(101−29, 101, 298)-Net over F₃ — Digital

Digital (72, 101, 298)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(101−29, 101, 7721)-Net in Base 3 — Upper bound on s

There is no (72, 101, 7722)-net in base 3, because

1 times m-reduction [i] would yield (72, 100, 7722)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 516227 695220 987637 729716 939501 376965 549003 011837 > 3¹⁰⁰ [i]