MinT - Best Known (88, 88+30, s)-Nets in Base 2

Best Known (88, 88+30, s)-Nets in Base 2

(88, 88+30, 135)-Net over F₂ — Constructive and digital

Digital (88, 118, 135)-net over F₂, using

2¹ times duplication [i] based on digital (87, 117, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 39, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(88, 88+30, 176)-Net over F₂ — Digital

Digital (88, 118, 176)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+30, 1477)-Net in Base 2 — Upper bound on s

There is no (88, 118, 1478)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 334379 271479 345685 405539 852859 554368 > 2¹¹⁸ [i]