MinT - Best Known (99−30, 99, s)-Nets in Base 3

Best Known (99−30, 99, s)-Nets in Base 3

(99−30, 99, 156)-Net over F₃ — Constructive and digital

Digital (69, 99, 156)-net over F₃, using

trace code for nets [i] based on digital (3, 33, 52)-net over F₂₇, using
- net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
    - a function field by SÃ©mirat [i]

(99−30, 99, 243)-Net over F₃ — Digital

Digital (69, 99, 243)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−30, 99, 4511)-Net in Base 3 — Upper bound on s

There is no (69, 99, 4512)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 171933 394068 114300 259632 443804 203458 293436 955521 > 3⁹⁹ [i]