MinT - Best Known (152, 152+108, s)-Nets in Base 2

Best Known (152, 152+108, s)-Nets in Base 2

(152, 152+108, 76)-Net over F₂ — Constructive and digital

Digital (152, 260, 76)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (39, 93, 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 (59, 167, 43)-net over F₂, using
  - net from sequence [i] based on digital (59, 42)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 54, N(F)Â =Â 42, and 1 place with degree 6 [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]

(152, 152+108, 106)-Net over F₂ — Digital

Digital (152, 260, 106)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(152, 152+108, 514)-Net in Base 2 — Upper bound on s

There is no (152, 260, 515)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 974525 245279 695365 242448 680731 474235 623380 986334 859891 772679 628220 659737 263744 > 2²⁶⁰ [i]