MinT - Best Known (226−98, 226, s)-Nets in Base 2

Best Known (226−98, 226, s)-Nets in Base 2

(226−98, 226, 66)-Net over F₂ — Constructive and digital

Digital (128, 226, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 113, 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]

(226−98, 226, 85)-Net over F₂ — Digital

Digital (128, 226, 85)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−98, 226, 399)-Net in Base 2 — Upper bound on s

There is no (128, 226, 400)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 116 677308 112093 916509 891673 383365 577823 754875 630216 488666 133156 628552 > 2²²⁶ [i]