MinT - Best Known (208−103, 208, s)-Nets in Base 3

Best Known (208−103, 208, s)-Nets in Base 3

(208−103, 208, 74)-Net over F₃ — Constructive and digital

Digital (105, 208, 74)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (27, 78, 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, 130, 37)-net over F₃, using
  - net from sequence [i] based on digital (27, 36)-sequence over F₃ (see above)

(208−103, 208, 106)-Net over F₃ — Digital

Digital (105, 208, 106)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(208−103, 208, 808)-Net in Base 3 — Upper bound on s

There is no (105, 208, 809)-net in base 3, because

1 times m-reduction [i] would yield (105, 207, 809)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 599 063451 083829 070613 015979 079346 801822 462088 267939 301992 584640 407559 767148 849120 099093 027929 022523 > 3²⁰⁷ [i]