MinT - Best Known (99, 141, s)-Nets in Base 3

Best Known (99, 141, s)-Nets in Base 3

(99, 141, 204)-Net over F₃ — Constructive and digital

Digital (99, 141, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 47, 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]

(99, 141, 338)-Net over F₃ — Digital

Digital (99, 141, 338)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 141, 6913)-Net in Base 3 — Upper bound on s

There is no (99, 141, 6914)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 817889 134856 549217 992111 354464 716948 112351 678190 728785 800019 375741 > 3¹⁴¹ [i]