MinT - Best Known (94, 94+81, s)-Nets in Base 3

Best Known (94, 94+81, s)-Nets in Base 3

(94, 94+81, 74)-Net over F₃ — Constructive and digital

Digital (94, 175, 74)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (27, 67, 37)-net over F₃, using
  - net from sequence [i] based on digital (27, 36)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 26, N(F)Â =Â 36, and 1 place with degree 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
2. digital (27, 108, 37)-net over F₃, using
  - net from sequence [i] based on digital (27, 36)-sequence over F₃ (see above)

(94, 94+81, 111)-Net over F₃ — Digital

Digital (94, 175, 111)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(94, 94+81, 899)-Net in Base 3 — Upper bound on s

There is no (94, 175, 900)-net in base 3, because

1 times m-reduction [i] would yield (94, 174, 900)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 107866 412439 719048 224385 586860 644938 552302 827227 280991 561889 203671 586525 618064 120513 > 3¹⁷⁴ [i]