MinT - Best Known (52, 52+21, s)-Nets in Base 4

Best Known (52, 52+21, s)-Nets in Base 4

(52, 52+21, 312)-Net over F₄ — Constructive and digital

Digital (52, 73, 312)-net over F₄, using

4¹ times duplication [i] based on digital (51, 72, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 24, 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]

(52, 52+21, 446)-Net over F₄ — Digital

Digital (52, 73, 446)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+21, 32627)-Net in Base 4 — Upper bound on s

There is no (52, 73, 32628)-net in base 4, because

1 times m-reduction [i] would yield (52, 72, 32628)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 22 304704 902398 276698 431423 322439 262513 355846 > 4⁷² [i]