MinT - Best Known (108−33, 108, s)-Nets in Base 3

Best Known (108−33, 108, s)-Nets in Base 3

(108−33, 108, 156)-Net over F₃ — Constructive and digital

Digital (75, 108, 156)-net over F₃, using

trace code for nets [i] based on digital (3, 36, 52)-net over F₂₇, using
- net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
    - a function field by SÃ©mirat [i]

(108−33, 108, 252)-Net over F₃ — Digital

Digital (75, 108, 252)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(108−33, 108, 5259)-Net in Base 3 — Upper bound on s

There is no (75, 108, 5260)-net in base 3, because

1 times m-reduction [i] would yield (75, 107, 5260)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1127 335778 862766 702128 349711 074892 122467 845353 488001 > 3¹⁰⁷ [i]