MinT - Best Known (195−95, 195, s)-Nets in Base 3

Best Known (195−95, 195, s)-Nets in Base 3

(195−95, 195, 73)-Net over F₃ — Constructive and digital

Digital (100, 195, 73)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (26, 73, 36)-net over F₃, using
  - net from sequence [i] based on digital (26, 35)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [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, 122, 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]

(195−95, 195, 105)-Net over F₃ — Digital

Digital (100, 195, 105)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(195−95, 195, 810)-Net in Base 3 — Upper bound on s

There is no (100, 195, 811)-net in base 3, because

1 times m-reduction [i] would yield (100, 194, 811)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 374 447683 951339 889148 987320 654582 139941 974701 294076 999439 782510 373353 593938 749740 770776 670547 > 3¹⁹⁴ [i]