MinT - Best Known (90−25, 90, s)-Nets in Base 3

Best Known (90−25, 90, s)-Nets in Base 3

(90−25, 90, 204)-Net over F₃ — Constructive and digital

Digital (65, 90, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 30, 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]

(90−25, 90, 312)-Net over F₃ — Digital

Digital (65, 90, 312)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−25, 90, 9129)-Net in Base 3 — Upper bound on s

There is no (65, 90, 9130)-net in base 3, because

1 times m-reduction [i] would yield (65, 89, 9130)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 912252 928952 995059 333219 463982 325394 591609 > 3⁸⁹ [i]