MinT - Best Known (81, 81+33, s)-Nets in Base 3

Best Known (81, 81+33, s)-Nets in Base 3

(81, 81+33, 204)-Net over F₃ — Constructive and digital

Digital (81, 114, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 38, 68)-net over F₂₇, using
- net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
    - a function field by SÃ©mirat [i]

(81, 81+33, 316)-Net over F₃ — Digital

Digital (81, 114, 316)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 81+33, 7949)-Net in Base 3 — Upper bound on s

There is no (81, 114, 7950)-net in base 3, because

1 times m-reduction [i] would yield (81, 113, 7950)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 822731 261602 316949 993555 342907 156559 790090 175561 557921 > 3¹¹³ [i]