MinT - Best Known (10, 10+16, s)-Nets in Base 2

Best Known (10, 10+16, s)-Nets in Base 2

(10, 10+16, 12)-Net over F₂ — Constructive and digital

Digital (10, 26, 12)-net over F₂, using

t-expansion [i] based on digital (9, 26, 12)-net over F₂, using
- net from sequence [i] based on digital (9, 11)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 9 and N(F) ≥ 12, using
    - an explicitly constructive algebraic function field [i]
- Niederreiterâ€“Xing sequence (PirÅ¡iÄ‡ implementation) with equidistant coordinate [i]

(10, 10+16, 13)-Net over F₂ — Digital

Digital (10, 26, 13)-net over F₂, using

net from sequence [i] based on digital (10, 12)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 10 and N(F) ≥ 13, using
  - a curve from the manYPoints database [i]

(10, 10+16, 22)-Net in Base 2 — Upper bound on s

There is no (10, 26, 23)-net in base 2, because

extracting embedded OOA [i] would yield OOA(2²⁶, 23, S₂, 2, 16), but
- the linear programming bound for OOAs shows that MÂ â‰¥ 2 593968 962952 148395 896363 548672 / 33028 192399 649776 116653 > 2²⁶ [i]