MinT - Best Known (76, 76+42, s)-Nets in Base 2

Best Known (76, 76+42, s)-Nets in Base 2

(76, 76+42, 66)-Net over F₂ — Constructive and digital

Digital (76, 118, 66)-net over F₂, using

4 times m-reduction [i] based on digital (76, 122, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 61, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(76, 76+42, 80)-Net over F₂ — Digital

Digital (76, 118, 80)-net over F₂, using

trace code for nets [i] based on digital (17, 59, 40)-net over F₄, using
- net from sequence [i] based on digital (17, 39)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 17 and N(F) ≥ 40, using
    - Drinfeld modules of rank 1 [i]

(76, 76+42, 396)-Net in Base 2 — Upper bound on s

There is no (76, 118, 397)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 339585 334469 274232 085471 908521 946448 > 2¹¹⁸ [i]