MinT - Best Known (99, 99+41, s)-Nets in Base 3

Best Known (99, 99+41, s)-Nets in Base 3

(99, 99+41, 204)-Net over F₃ — Constructive and digital

Digital (99, 140, 204)-net over F₃, using

1 times m-reduction [i] based on 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, 99+41, 356)-Net over F₃ — Digital

Digital (99, 140, 356)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 99+41, 8575)-Net in Base 3 — Upper bound on s

There is no (99, 140, 8576)-net in base 3, because

1 times m-reduction [i] would yield (99, 139, 8576)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 088716 538616 810131 694998 113225 592194 887115 696595 944767 420184 867841 > 3¹³⁹ [i]