MinT - Best Known (183, 183+63, s)-Nets in Base 3

Best Known (183, 183+63, s)-Nets in Base 3

(183, 183+63, 324)-Net over F₃ — Constructive and digital

Digital (183, 246, 324)-net over F₃, using

t-expansion [i] based on digital (182, 246, 324)-net over F₃, using
- trace code for nets [i] based on digital (18, 82, 108)-net over F₂₇, using
  - net from sequence [i] based on digital (18, 107)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 18 and N(F) ≥ 108, using
      - F₃ from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F₂₇ [i]

(183, 183+63, 920)-Net over F₃ — Digital

Digital (183, 246, 920)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(183, 183+63, 36596)-Net in Base 3 — Upper bound on s

There is no (183, 246, 36597)-net in base 3, because

1 times m-reduction [i] would yield (183, 245, 36597)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 785 108691 484455 949265 971462 673700 133590 389583 886973 189107 603517 544544 053102 781517 474424 944127 732470 047237 394702 472315 > 3²⁴⁵ [i]