MinT - Best Known (238−55, 238, s)-Nets in Base 2

Best Known (238−55, 238, s)-Nets in Base 2

(238−55, 238, 203)-Net over F₂ — Constructive and digital

Digital (183, 238, 203)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (4, 31, 8)-net over F₂, using
  - net from sequence [i] based on digital (4, 7)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 4 and N(F) ≥ 8, using
      - an explicitly constructive algebraic function field [i]
  - Niederreiterâ€“Xing sequence (PirÅ¡iÄ‡ implementation) with equidistant coordinate [i]
2. digital (152, 207, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 69, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
        the Suzuki function field over F₈ [i]

(238−55, 238, 399)-Net over F₂ — Digital

Digital (183, 238, 399)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−55, 238, 4755)-Net in Base 2 — Upper bound on s

There is no (183, 238, 4756)-net in base 2, because

1 times m-reduction [i] would yield (183, 237, 4756)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 222015 561545 517399 139250 160023 985603 404639 009527 356860 098878 236444 000368 > 2²³⁷ [i]