MinT - Best Known (242−106, 242, s)-Nets in Base 2

Best Known (242−106, 242, s)-Nets in Base 2

(242−106, 242, 66)-Net over F₂ — Constructive and digital

Digital (136, 242, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 121, 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]

(242−106, 242, 88)-Net over F₂ — Digital

Digital (136, 242, 88)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−106, 242, 414)-Net in Base 2 — Upper bound on s

There is no (136, 242, 415)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7 671200 618360 586279 916574 895371 529159 125840 727297 516190 922781 186758 893168 > 2²⁴² [i]