MinT - Best Known (99, 99+75, s)-Nets in Base 3

Best Known (99, 99+75, s)-Nets in Base 3

(99, 99+75, 80)-Net over F₃ — Constructive and digital

Digital (99, 174, 80)-net over F₃, using

8 times m-reduction [i] based on digital (99, 182, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 91, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(99, 99+75, 135)-Net over F₃ — Digital

Digital (99, 174, 135)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 99+75, 1210)-Net in Base 3 — Upper bound on s

There is no (99, 174, 1211)-net in base 3, because

1 times m-reduction [i] would yield (99, 173, 1211)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 35254 799597 605138 459307 646705 121767 573489 520230 470387 412116 443852 263829 017223 166447 > 3¹⁷³ [i]