MinT - Best Known (90, 90+36, s)-Nets in Base 3

Best Known (90, 90+36, s)-Nets in Base 3

(90, 90+36, 228)-Net over F₃ — Constructive and digital

Digital (90, 126, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 42, 76)-net over F₂₇, using
- net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(90, 90+36, 357)-Net over F₃ — Digital

Digital (90, 126, 357)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+36, 8241)-Net in Base 3 — Upper bound on s

There is no (90, 126, 8242)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 310243 042804 456383 019050 418297 266343 280160 223307 743371 884885 > 3¹²⁶ [i]