MinT - Best Known (109, 109+50, s)-Nets in Base 4

Best Known (109, 109+50, s)-Nets in Base 4

(109, 109+50, 312)-Net over F₄ — Constructive and digital

Digital (109, 159, 312)-net over F₄, using

trace code for nets [i] based on digital (3, 53, 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]

(109, 109+50, 566)-Net over F₄ — Digital

Digital (109, 159, 566)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+50, 22867)-Net in Base 4 — Upper bound on s

There is no (109, 159, 22868)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 534240 281250 643335 181662 478867 760719 657991 282176 058097 400255 058085 162100 826238 735822 920831 661256 > 4¹⁵⁹ [i]