MinT - Best Known (228−90, 228, s)-Nets in Base 2

Best Known (228−90, 228, s)-Nets in Base 2

(228−90, 228, 75)-Net over F₂ — Constructive and digital

Digital (138, 228, 75)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (39, 84, 33)-net over F₂, using
  - net from sequence [i] based on digital (39, 32)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]
2. digital (54, 144, 42)-net over F₂, using
  - net from sequence [i] based on digital (54, 41)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
      - an explicitly constructive algebraic function field [i]

(228−90, 228, 106)-Net over F₂ — Digital

Digital (138, 228, 106)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−90, 228, 527)-Net in Base 2 — Upper bound on s

There is no (138, 228, 528)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 465 303095 346117 463295 398731 364383 362036 353897 897404 034646 956686 078288 > 2²²⁸ [i]