MinT - Best Known (105, 105+93, s)-Nets in Base 3

Best Known (105, 105+93, s)-Nets in Base 3

(105, 105+93, 75)-Net over F₃ — Constructive and digital

Digital (105, 198, 75)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (27, 73, 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 (32, 125, 38)-net over F₃, using
  - net from sequence [i] based on digital (32, 37)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 32 and N(F) ≥ 38, using
      - an explicitly constructive algebraic function field [i]

(105, 105+93, 118)-Net over F₃ — Digital

Digital (105, 198, 118)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 105+93, 949)-Net in Base 3 — Upper bound on s

There is no (105, 198, 950)-net in base 3, because

1 times m-reduction [i] would yield (105, 197, 950)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9993 178219 121934 834752 099016 393856 017314 521313 699894 383421 274205 967239 003886 234917 922414 012997 > 3¹⁹⁷ [i]