MinT - Best Known (105−34, 105, s)-Nets in Base 4

Best Known (105−34, 105, s)-Nets in Base 4

(105−34, 105, 240)-Net over F₄ — Constructive and digital

Digital (71, 105, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 35, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(105−34, 105, 364)-Net over F₄ — Digital

Digital (71, 105, 364)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−34, 105, 12501)-Net in Base 4 — Upper bound on s

There is no (71, 105, 12502)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1647 051570 180905 790549 946237 780004 042647 332378 089970 075006 023155 > 4¹⁰⁵ [i]