MinT - Best Known (100−35, 100, s)-Nets in Base 2

Best Known (100−35, 100, s)-Nets in Base 2

(100−35, 100, 66)-Net over F₂ — Constructive and digital

Digital (65, 100, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 50, 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]

(100−35, 100, 72)-Net over F₂ — Digital

Digital (65, 100, 72)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(100−35, 100, 382)-Net in Base 2 — Upper bound on s

There is no (65, 100, 383)-net in base 2, because

1 times m-reduction [i] would yield (65, 99, 383)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 657579 191363 731224 361962 648560 > 2⁹⁹ [i]