MinT - Best Known (180−75, 180, s)-Nets in Base 2

Best Known (180−75, 180, s)-Nets in Base 2

(180−75, 180, 66)-Net over F₂ — Constructive and digital

Digital (105, 180, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 90, 33)-net over F₄, using
- net from sequence [i] based on digital (15, 32)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(180−75, 180, 77)-Net over F₂ — Digital

Digital (105, 180, 77)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(180−75, 180, 367)-Net in Base 2 — Upper bound on s

There is no (105, 180, 368)-net in base 2, because

1 times m-reduction [i] would yield (105, 179, 368)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 829204 246555 031627 745044 884135 557546 021160 090797 105687 > 2¹⁷⁹ [i]