MinT - Best Known (155, 155+40, s)-Nets in Base 4

Best Known (155, 155+40, s)-Nets in Base 4

(155, 155+40, 1061)-Net over F₄ — Constructive and digital

Digital (155, 195, 1061)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (15, 35, 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]
2. digital (120, 160, 1028)-net over F₄, using
  - trace code for nets [i] based on digital (0, 40, 257)-net over F₂₅₆, using
    - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
      - Niederreiter sequence [i]

(155, 155+40, 5275)-Net over F₄ — Digital

Digital (155, 195, 5275)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(155, 155+40, 2052421)-Net in Base 4 — Upper bound on s

There is no (155, 195, 2052422)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2521 750521 285804 474090 963425 979736 940857 692002 243972 948945 876515 991800 561954 539387 994442 750343 643999 381221 903232 870636 > 4¹⁹⁵ [i]