MinT - Best Known (259−49, 259, s)-Nets in Base 2

Best Known (259−49, 259, s)-Nets in Base 2

(259−49, 259, 294)-Net over F₂ — Constructive and digital

Digital (210, 259, 294)-net over F₂, using

2¹ times duplication [i] based on digital (209, 258, 294)-net over F₂, using
- trace code for nets [i] based on digital (37, 86, 98)-net over F₈, using
  - net from sequence [i] based on digital (37, 97)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
      - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(259−49, 259, 766)-Net over F₂ — Digital

Digital (210, 259, 766)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(259−49, 259, 16846)-Net in Base 2 — Upper bound on s

There is no (210, 259, 16847)-net in base 2, because

1 times m-reduction [i] would yield (210, 258, 16847)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 463186 075303 524840 841621 513700 418781 207159 777516 800282 248489 120011 103406 476548 > 2²⁵⁸ [i]