MinT - Best Known (203−87, 203, s)-Nets in Base 2

Best Known (203−87, 203, s)-Nets in Base 2

(203−87, 203, 62)-Net over F₂ — Constructive and digital

Digital (116, 203, 62)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (19, 62, 20)-net over F₂, using
  - net from sequence [i] based on digital (19, 19)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 19 and N(F) ≥ 20, using
      - an explicitly constructive algebraic function field [i]
2. digital (54, 141, 42)-net over F₂, using
  - net from sequence [i] based on digital (54, 41)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
      - an explicitly constructive algebraic function field [i]

(203−87, 203, 80)-Net over F₂ — Digital

Digital (116, 203, 80)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(203−87, 203, 378)-Net in Base 2 — Upper bound on s

There is no (116, 203, 379)-net in base 2, because

1 times m-reduction [i] would yield (116, 202, 379)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7 027518 461283 820382 078975 324143 503869 849449 789809 978277 605418 > 2²⁰² [i]