MinT - Best Known (198−84, 198, s)-Nets in Base 2

Best Known (198−84, 198, s)-Nets in Base 2

(198−84, 198, 66)-Net over F₂ — Constructive and digital

Digital (114, 198, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 99, 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]

(198−84, 198, 80)-Net over F₂ — Digital

Digital (114, 198, 80)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−84, 198, 374)-Net in Base 2 — Upper bound on s

There is no (114, 198, 375)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 410619 283156 368038 612318 265514 246506 642848 566630 794321 991566 > 2¹⁹⁸ [i]