MinT - Best Known (79, 110, s)-Nets in Base 3

Best Known (79, 110, s)-Nets in Base 3

(79, 110, 204)-Net over F₃ — Constructive and digital

Digital (79, 110, 204)-net over F₃, using

1 times m-reduction [i] based on digital (79, 111, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 37, 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]

(79, 110, 339)-Net over F₃ — Digital

Digital (79, 110, 339)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(79, 110, 9400)-Net in Base 3 — Upper bound on s

There is no (79, 110, 9401)-net in base 3, because

1 times m-reduction [i] would yield (79, 109, 9401)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10153 006683 848453 010917 729531 912847 853113 680716 085067 > 3¹⁰⁹ [i]