MinT - Best Known (228−70, 228, s)-Nets in Base 3

Best Known (228−70, 228, s)-Nets in Base 3

(228−70, 228, 228)-Net over F₃ — Constructive and digital

Digital (158, 228, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 76, 76)-net over F₂₇, using
- net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(228−70, 228, 462)-Net over F₃ — Digital

Digital (158, 228, 462)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−70, 228, 8885)-Net in Base 3 — Upper bound on s

There is no (158, 228, 8886)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 100203 726350 263917 678540 971447 637239 943165 618180 985933 652718 398826 073224 041642 950079 518693 897426 318858 143201 > 3²²⁸ [i]