MinT - Best Known (168−55, 168, s)-Nets in Base 4

Best Known (168−55, 168, s)-Nets in Base 4

(168−55, 168, 240)-Net over F₄ — Constructive and digital

Digital (113, 168, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 56, 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]

(168−55, 168, 507)-Net over F₄ — Digital

Digital (113, 168, 507)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−55, 168, 19259)-Net in Base 4 — Upper bound on s

There is no (113, 168, 19260)-net in base 4, because

1 times m-reduction [i] would yield (113, 167, 19260)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35026 063724 202661 213576 576160 048560 227628 548153 830940 790089 406217 140616 379732 469110 843015 052582 908469 > 4¹⁶⁷ [i]