MinT - Best Known (138−42, 138, s)-Nets in Base 3

Best Known (138−42, 138, s)-Nets in Base 3

(138−42, 138, 192)-Net over F₃ — Constructive and digital

Digital (96, 138, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 46, 64)-net over F₂₇, using
- net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(138−42, 138, 309)-Net over F₃ — Digital

Digital (96, 138, 309)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−42, 138, 5906)-Net in Base 3 — Upper bound on s

There is no (96, 138, 5907)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 697498 467976 725612 539923 342254 107044 736113 995122 929592 836906 228095 > 3¹³⁸ [i]