MinT - Best Known (81, 81+34, s)-Nets in Base 3

Best Known (81, 81+34, s)-Nets in Base 3

(81, 81+34, 192)-Net over F₃ — Constructive and digital

Digital (81, 115, 192)-net over F₃, using

3¹ times duplication [i] based on digital (80, 114, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 38, 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]

(81, 81+34, 296)-Net over F₃ — Digital

Digital (81, 115, 296)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 81+34, 6043)-Net in Base 3 — Upper bound on s

There is no (81, 115, 6044)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7 397113 360923 548831 188300 063653 607613 795990 671236 235065 > 3¹¹⁵ [i]