MinT - Best Known (133−30, 133, s)-Nets in Base 2

Best Known (133−30, 133, s)-Nets in Base 2

(133−30, 133, 195)-Net over F₂ — Constructive and digital

Digital (103, 133, 195)-net over F₂, using

2¹ times duplication [i] based on digital (102, 132, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 44, 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]

(133−30, 133, 265)-Net over F₂ — Digital

Digital (103, 133, 265)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−30, 133, 2976)-Net in Base 2 — Upper bound on s

There is no (103, 133, 2977)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 10914 130937 285704 913508 197120 277300 098048 > 2¹³³ [i]