MinT - Best Known (103, 103+102, s)-Nets in Base 2

Best Known (103, 103+102, s)-Nets in Base 2

(103, 103+102, 55)-Net over F₂ — Constructive and digital

Digital (103, 205, 55)-net over F₂, using

t-expansion [i] based on digital (100, 205, 55)-net over F₂, using
- net from sequence [i] based on digital (100, 54)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 69, N(F)Â =Â 48, 1 place with degree 2, and 6 places with degree 6 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]

(103, 103+102, 65)-Net over F₂ — Digital

Digital (103, 205, 65)-net over F₂, using

t-expansion [i] based on digital (95, 205, 65)-net over F₂, using
- net from sequence [i] based on digital (95, 64)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 95 and N(F) ≥ 65, using
    - Drinfeld modules of rank 1 [i]

(103, 103+102, 217)-Net in Base 2 — Upper bound on s

There is no (103, 205, 218)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2²⁰⁵, 218, S₂, 102), but
- the linear programming bound shows that MÂ â‰¥ 272331 004236 659599 976647 399713 241508 574642 785762 357467 384194 793472 / 3835 > 2²⁰⁵ [i]