MinT - Best Known (235−196, 235, s)-Nets in Base 2

Best Known (235−196, 235, s)-Nets in Base 2

(235−196, 235, 33)-Net over F₂ — Constructive and digital

Digital (39, 235, 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]

(235−196, 235, 48)-Net in Base 2 — Upper bound on s

There is no (39, 235, 49)-net in base 2, because

extracting embedded OOA [i] would yield OOA(2²³⁵, 49, S₂, 5, 196), but
- the LP bound with quadratic polynomials shows that MÂ â‰¥ 64 489917 864411 028029 790358 777116 525827 703162 235960 091971 438626 347180 621824 / 985 > 2²³⁵ [i]