MinT - Best Known (43−20, 43, s)-Nets in Base 3

Best Known (43−20, 43, s)-Nets in Base 3

(43−20, 43, 32)-Net over F₃ — Constructive and digital

Digital (23, 43, 32)-net over F₃, using

t-expansion [i] based on digital (21, 43, 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]

(43−20, 43, 38)-Net over F₃ — Digital

Digital (23, 43, 38)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(43−20, 43, 245)-Net in Base 3 — Upper bound on s

There is no (23, 43, 246)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 332 636275 192785 793821 > 3⁴³ [i]