MinT - Best Known (165−52, 165, s)-Nets in Base 4

Best Known (165−52, 165, s)-Nets in Base 4

(165−52, 165, 312)-Net over F₄ — Constructive and digital

Digital (113, 165, 312)-net over F₄, using

trace code for nets [i] based on digital (3, 55, 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]

(165−52, 165, 579)-Net over F₄ — Digital

Digital (113, 165, 579)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(165−52, 165, 23256)-Net in Base 4 — Upper bound on s

There is no (113, 165, 23257)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2188 759821 487451 399698 623865 018087 925029 073432 074111 401855 756291 519277 248116 823382 017682 598540 871088 > 4¹⁶⁵ [i]