MinT - Best Known (156−45, 156, s)-Nets in Base 3

Best Known (156−45, 156, s)-Nets in Base 3

(156−45, 156, 246)-Net over F₃ — Constructive and digital

Digital (111, 156, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 52, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(156−45, 156, 409)-Net over F₃ — Digital

Digital (111, 156, 409)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(156−45, 156, 10386)-Net in Base 3 — Upper bound on s

There is no (111, 156, 10387)-net in base 3, because

1 times m-reduction [i] would yield (111, 155, 10387)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 90 035856 742809 191926 099039 544664 681463 494040 544301 728553 285037 374128 383389 > 3¹⁵⁵ [i]