MinT - Best Known (100−29, 100, s)-Nets in Base 3

Best Known (100−29, 100, s)-Nets in Base 3

(100−29, 100, 192)-Net over F₃ — Constructive and digital

Digital (71, 100, 192)-net over F₃, using

3¹ times duplication [i] based on digital (70, 99, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 33, 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]

(100−29, 100, 285)-Net over F₃ — Digital

Digital (71, 100, 285)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(100−29, 100, 7137)-Net in Base 3 — Upper bound on s

There is no (71, 100, 7138)-net in base 3, because

1 times m-reduction [i] would yield (71, 99, 7138)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 172013 494312 273081 040350 219467 973408 350516 117453 > 3⁹⁹ [i]