MinT - Best Known (203−79, 203, s)-Nets in Base 2

Best Known (203−79, 203, s)-Nets in Base 2

(203−79, 203, 68)-Net over F₂ — Constructive and digital

Digital (124, 203, 68)-net over F₂, using

3 times m-reduction [i] based on digital (124, 206, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 103, 34)-net over F₄, using
  - net from sequence [i] based on digital (21, 33)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
      - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(203−79, 203, 99)-Net over F₂ — Digital

Digital (124, 203, 99)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(203−79, 203, 502)-Net in Base 2 — Upper bound on s

There is no (124, 203, 503)-net in base 2, because

1 times m-reduction [i] would yield (124, 202, 503)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 622725 138804 654094 301587 647659 219102 625349 393304 365302 605742 > 2²⁰² [i]