MinT - Best Known (99, 137, s)-Nets in Base 3

Best Known (99, 137, s)-Nets in Base 3

(99, 137, 246)-Net over F₃ — Constructive and digital

Digital (99, 137, 246)-net over F₃, using

1 times m-reduction [i] based on digital (99, 138, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 46, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(99, 137, 424)-Net over F₃ — Digital

Digital (99, 137, 424)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 137, 10908)-Net in Base 3 — Upper bound on s

There is no (99, 137, 10909)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 232466 777105 791921 274695 886417 456625 677271 846951 041621 400271 544523 > 3¹³⁷ [i]