MinT - Best Known (89, 89+59, s)-Nets in Base 2

Best Known (89, 89+59, s)-Nets in Base 2

(89, 89+59, 66)-Net over F₂ — Constructive and digital

Digital (89, 148, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 74, 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]

(89, 89+59, 73)-Net over F₂ — Digital

Digital (89, 148, 73)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 89+59, 350)-Net in Base 2 — Upper bound on s

There is no (89, 148, 351)-net in base 2, because

1 times m-reduction [i] would yield (89, 147, 351)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 181 019640 501062 102565 773532 681025 884652 488236 > 2¹⁴⁷ [i]