MinT - Best Known (166−75, 166, s)-Nets in Base 3

Best Known (166−75, 166, s)-Nets in Base 3

(166−75, 166, 80)-Net over F₃ — Constructive and digital

Digital (91, 166, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 83, 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]

(166−75, 166, 113)-Net over F₃ — Digital

Digital (91, 166, 113)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−75, 166, 947)-Net in Base 3 — Upper bound on s

There is no (91, 166, 948)-net in base 3, because

1 times m-reduction [i] would yield (91, 165, 948)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5 486689 481509 419784 213478 485981 176474 610615 155613 592022 432443 107772 768988 287049 > 3¹⁶⁵ [i]