MinT - Best Known (220−41, 220, s)-Nets in Base 2

Best Known (220−41, 220, s)-Nets in Base 2

(220−41, 220, 320)-Net over F₂ — Constructive and digital

Digital (179, 220, 320)-net over F₂, using

trace code for nets [i] based on digital (3, 44, 64)-net over F₃₂, using
- net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(220−41, 220, 705)-Net over F₂ — Digital

Digital (179, 220, 705)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−41, 220, 16398)-Net in Base 2 — Upper bound on s

There is no (179, 220, 16399)-net in base 2, because

1 times m-reduction [i] would yield (179, 219, 16399)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 842986 993834 303462 153250 772576 070850 336940 958647 798714 564249 445376 > 2²¹⁹ [i]