MinT - Best Known (79−19, 79, s)-Nets in Base 2

Best Known (79−19, 79, s)-Nets in Base 2

(79−19, 79, 102)-Net over F₂ — Constructive and digital

Digital (60, 79, 102)-net over F₂, using

2¹ times duplication [i] based on digital (59, 78, 102)-net over F₂, using
- trace code for nets [i] based on digital (7, 26, 34)-net over F₈, using
  - net from sequence [i] based on digital (7, 33)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]

(79−19, 79, 154)-Net over F₂ — Digital

Digital (60, 79, 154)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(79−19, 79, 1672)-Net in Base 2 — Upper bound on s

There is no (60, 79, 1673)-net in base 2, because

1 times m-reduction [i] would yield (60, 78, 1673)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 303285 689470 381870 645234 > 2⁷⁸ [i]