MinT - Best Known (48−24, 48, s)-Nets in Base 3

Best Known (48−24, 48, s)-Nets in Base 3

(48−24, 48, 32)-Net over F₃ — Constructive and digital

Digital (24, 48, 32)-net over F₃, using

t-expansion [i] based on digital (21, 48, 32)-net over F₃, using
- net from sequence [i] based on digital (21, 31)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
    - an explicitly constructive algebraic function field [i]

(48−24, 48, 34)-Net over F₃ — Digital

Digital (24, 48, 34)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(48−24, 48, 202)-Net in Base 3 — Upper bound on s

There is no (24, 48, 203)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 79987 991938 255049 631433 > 3⁴⁸ [i]