MinT - Best Known (231−68, 231, s)-Nets in Base 3

Best Known (231−68, 231, s)-Nets in Base 3

(231−68, 231, 264)-Net over F₃ — Constructive and digital

Digital (163, 231, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 77, 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]

(231−68, 231, 534)-Net over F₃ — Digital

Digital (163, 231, 534)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−68, 231, 11771)-Net in Base 3 — Upper bound on s

There is no (163, 231, 11772)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 164 314072 776742 034665 391489 146230 305539 644942 788325 217963 180488 450386 082784 900546 011967 069384 385305 406125 788681 > 3²³¹ [i]