MinT - Best Known (81, 81+35, s)-Nets in Base 4

Best Known (81, 81+35, s)-Nets in Base 4

(81, 81+35, 312)-Net over F₄ — Constructive and digital

Digital (81, 116, 312)-net over F₄, using

1 times m-reduction [i] based on digital (81, 117, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 39, 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]

(81, 81+35, 527)-Net over F₄ — Digital

Digital (81, 116, 527)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 81+35, 28273)-Net in Base 4 — Upper bound on s

There is no (81, 116, 28274)-net in base 4, because

1 times m-reduction [i] would yield (81, 115, 28274)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1726 407384 096750 822783 766453 486464 278943 280582 300011 380586 851649 413725 > 4¹¹⁵ [i]