MinT - Best Known (203−83, 203, s)-Nets in Base 2

Best Known (203−83, 203, s)-Nets in Base 2

(203−83, 203, 66)-Net over F₂ — Constructive and digital

Digital (120, 203, 66)-net over F₂, using

7 times m-reduction [i] based on digital (120, 210, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 105, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(203−83, 203, 89)-Net over F₂ — Digital

Digital (120, 203, 89)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(203−83, 203, 433)-Net in Base 2 — Upper bound on s

There is no (120, 203, 434)-net in base 2, because

1 times m-reduction [i] would yield (120, 202, 434)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 876651 811513 418108 443370 496733 200196 840990 919665 698822 696030 > 2²⁰² [i]