MinT - Best Known (76−34, 76, s)-Nets in Base 2

Best Known (76−34, 76, s)-Nets in Base 2

(76−34, 76, 33)-Net over F₂ — Constructive and digital

Digital (42, 76, 33)-net over F₂, using

t-expansion [i] based on digital (39, 76, 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]

(76−34, 76, 34)-Net over F₂ — Digital

Digital (42, 76, 34)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(76−34, 76, 125)-Net in Base 2 — Upper bound on s

There is no (42, 76, 126)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2⁷⁶, 126, S₂, 34), but
- the linear programming bound shows that MÂ â‰¥ 38 459620 016436 403553 321591 630765 416829 509898 862592 / 484 232223 153801 738635 105625 > 2⁷⁶ [i]