MinT - Best Known (241−79, 241, s)-Nets in Base 2

Best Known (241−79, 241, s)-Nets in Base 2

(241−79, 241, 112)-Net over F₂ — Constructive and digital

Digital (162, 241, 112)-net over F₂, using

17 times m-reduction [i] based on digital (162, 258, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 129, 56)-net over F₄, using
  - net from sequence [i] based on digital (33, 55)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
      - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(241−79, 241, 170)-Net over F₂ — Digital

Digital (162, 241, 170)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−79, 241, 1039)-Net in Base 2 — Upper bound on s

There is no (162, 241, 1040)-net in base 2, because

1 times m-reduction [i] would yield (162, 240, 1040)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 789877 136412 235796 696016 443438 714739 462046 749719 045846 567733 519618 036704 > 2²⁴⁰ [i]