MinT - Best Known (195−93, 195, s)-Nets in Base 3

Best Known (195−93, 195, s)-Nets in Base 3

(195−93, 195, 74)-Net over F₃ — Constructive and digital

Digital (102, 195, 74)-net over F₃, using

3 times m-reduction [i] based on digital (102, 198, 74)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (27, 75, 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, 123, 37)-net over F₃, using
    - net from sequence [i] based on digital (27, 36)-sequence over F₃ (see above)

(195−93, 195, 112)-Net over F₃ — Digital

Digital (102, 195, 112)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(195−93, 195, 880)-Net in Base 3 — Upper bound on s

There is no (102, 195, 881)-net in base 3, because

1 times m-reduction [i] would yield (102, 194, 881)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 364 838264 235832 632032 958353 916336 448294 729427 857335 864429 164376 553177 237338 525024 946970 823513 > 3¹⁹⁴ [i]