MinT - Best Known (62−30, 62, s)-Nets in Base 3

Best Known (62−30, 62, s)-Nets in Base 3

(62−30, 62, 38)-Net over F₃ — Constructive and digital

Digital (32, 62, 38)-net over F₃, using

net from sequence [i] based on digital (32, 37)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 32 and N(F) ≥ 38, using
  - an explicitly constructive algebraic function field [i]

(62−30, 62, 44)-Net over F₃ — Digital

Digital (32, 62, 44)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(62−30, 62, 286)-Net in Base 3 — Upper bound on s

There is no (32, 62, 287)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 382027 460887 939725 968130 593891 > 3⁶² [i]