MinT - Best Known (71, 71+61, s)-Nets in Base 3

Best Known (71, 71+61, s)-Nets in Base 3

(71, 71+61, 64)-Net over F₃ — Constructive and digital

Digital (71, 132, 64)-net over F₃, using

trace code for nets [i] based on digital (5, 66, 32)-net over F₉, using
- net from sequence [i] based on digital (5, 31)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
    - a function field by GarcÃa and Quoos [i]

(71, 71+61, 88)-Net over F₃ — Digital

Digital (71, 132, 88)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+61, 700)-Net in Base 3 — Upper bound on s

There is no (71, 132, 701)-net in base 3, because

1 times m-reduction [i] would yield (71, 131, 701)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 321 479773 088793 950762 383627 846334 224703 806592 756624 387292 087377 > 3¹³¹ [i]