MinT - Best Known (237−71, 237, s)-Nets in Base 3

Best Known (237−71, 237, s)-Nets in Base 3

(237−71, 237, 252)-Net over F₃ — Constructive and digital

Digital (166, 237, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 79, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(237−71, 237, 516)-Net over F₃ — Digital

Digital (166, 237, 516)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−71, 237, 11431)-Net in Base 3 — Upper bound on s

There is no (166, 237, 11432)-net in base 3, because

1 times m-reduction [i] would yield (166, 236, 11432)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 39979 784637 358012 123369 098623 659342 198129 876027 586401 102253 812940 644198 031072 723339 870603 435981 969651 889090 929697 > 3²³⁶ [i]