MinT - Best Known (159−44, 159, s)-Nets in Base 3

Best Known (159−44, 159, s)-Nets in Base 3

(159−44, 159, 264)-Net over F₃ — Constructive and digital

Digital (115, 159, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 53, 88)-net over F₂₇, using
- net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
    - a function field by SÃ©mirat [i]

(159−44, 159, 481)-Net over F₃ — Digital

Digital (115, 159, 481)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−44, 159, 12687)-Net in Base 3 — Upper bound on s

There is no (115, 159, 12688)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7289 674307 109847 511065 406589 955080 072795 384812 850901 249062 540881 696496 717153 > 3¹⁵⁹ [i]