MinT - Best Known (78, 78+25, s)-Nets in Base 2

Best Known (78, 78+25, s)-Nets in Base 2

(78, 78+25, 135)-Net over F₂ — Constructive and digital

Digital (78, 103, 135)-net over F₂, using

2¹ times duplication [i] based on digital (77, 102, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 34, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(78, 78+25, 179)-Net over F₂ — Digital

Digital (78, 103, 179)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+25, 1897)-Net in Base 2 — Upper bound on s

There is no (78, 103, 1898)-net in base 2, because

1 times m-reduction [i] would yield (78, 102, 1898)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 091595 804488 402388 365457 006568 > 2¹⁰² [i]