MinT - Best Known (58, 58+41, s)-Nets in Base 2

Best Known (58, 58+41, s)-Nets in Base 2

(58, 58+41, 42)-Net over F₂ — Constructive and digital

Digital (58, 99, 42)-net over F₂, using

t-expansion [i] based on digital (54, 99, 42)-net over F₂, using
- net from sequence [i] based on digital (54, 41)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
    - an explicitly constructive algebraic function field [i]

(58, 58+41, 49)-Net over F₂ — Digital

Digital (58, 99, 49)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+41, 219)-Net in Base 2 — Upper bound on s

There is no (58, 99, 220)-net in base 2, because

1 times m-reduction [i] would yield (58, 98, 220)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 318369 144640 082843 392564 093702 > 2⁹⁸ [i]