MinT - Best Known (248−134, 248, s)-Nets in Base 3

Best Known (248−134, 248, s)-Nets in Base 3

(248−134, 248, 74)-Net over F₃ — Constructive and digital

Digital (114, 248, 74)-net over F₃, using

t-expansion [i] based on digital (107, 248, 74)-net over F₃, using
- net from sequence [i] based on digital (107, 73)-sequence over F₃, using
  - base reduction for sequences [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(248−134, 248, 120)-Net over F₃ — Digital

Digital (114, 248, 120)-net over F₃, using

t-expansion [i] based on digital (113, 248, 120)-net over F₃, using
- net from sequence [i] based on digital (113, 119)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 113 and N(F) ≥ 120, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(248−134, 248, 688)-Net in Base 3 — Upper bound on s

There is no (114, 248, 689)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 22843 295950 581928 489751 257299 226322 878880 664030 395445 037823 773703 043724 121989 932154 443997 549328 718275 130654 197280 025179 > 3²⁴⁸ [i]