MinT - Best Known (103, 103+47, s)-Nets in Base 4

Best Known (103, 103+47, s)-Nets in Base 4

(103, 103+47, 312)-Net over F₄ — Constructive and digital

Digital (103, 150, 312)-net over F₄, using

trace code for nets [i] based on digital (3, 50, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(103, 103+47, 548)-Net over F₄ — Digital

Digital (103, 150, 548)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(103, 103+47, 24963)-Net in Base 4 — Upper bound on s

There is no (103, 150, 24964)-net in base 4, because

1 times m-reduction [i] would yield (103, 149, 24964)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 509312 725475 400663 293706 002024 819564 374160 140262 570602 017337 449737 387998 257757 516675 698592 > 4¹⁴⁹ [i]