MinT - Best Known (99, 99+63, s)-Nets in Base 3

Best Known (99, 99+63, s)-Nets in Base 3

(99, 99+63, 148)-Net over F₃ — Constructive and digital

Digital (99, 162, 148)-net over F₃, using

2 times m-reduction [i] based on digital (99, 164, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 82, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(99, 99+63, 169)-Net over F₃ — Digital

Digital (99, 162, 169)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 99+63, 1835)-Net in Base 3 — Upper bound on s

There is no (99, 162, 1836)-net in base 3, because

1 times m-reduction [i] would yield (99, 161, 1836)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 65657 917328 746783 347693 239837 247838 675537 309740 026686 145756 646680 576034 490769 > 3¹⁶¹ [i]