MinT - Best Known (84, 84+64, s)-Nets in Base 2

Best Known (84, 84+64, s)-Nets in Base 2

(84, 84+64, 54)-Net over F₂ — Constructive and digital

Digital (84, 148, 54)-net over F₂, using

trace code for nets [i] based on digital (10, 74, 27)-net over F₄, using
- net from sequence [i] based on digital (10, 26)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
    - an explicitly constructive algebraic function field [i]

(84, 84+64, 60)-Net over F₂ — Digital

Digital (84, 148, 60)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+64, 271)-Net in Base 2 — Upper bound on s

There is no (84, 148, 272)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 390 248081 291667 499948 490164 185376 881807 920856 > 2¹⁴⁸ [i]