MinT - Best Known (160, 160+68, s)-Nets in Base 3

Best Known (160, 160+68, s)-Nets in Base 3

(160, 160+68, 252)-Net over F₃ — Constructive and digital

Digital (160, 228, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 76, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(160, 160+68, 506)-Net over F₃ — Digital

Digital (160, 228, 506)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(160, 160+68, 10680)-Net in Base 3 — Upper bound on s

There is no (160, 228, 10681)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 079109 407002 375008 939757 129698 962924 278728 943609 579671 349204 826056 396539 109928 035817 648522 298158 833427 189305 > 3²²⁸ [i]