MinT - Best Known (85−27, 85, s)-Nets in Base 4

Best Known (85−27, 85, s)-Nets in Base 4

(85−27, 85, 240)-Net over F₄ — Constructive and digital

Digital (58, 85, 240)-net over F₄, using

4¹ times duplication [i] based on digital (57, 84, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 28, 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]

(85−27, 85, 340)-Net over F₄ — Digital

Digital (58, 85, 340)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(85−27, 85, 14662)-Net in Base 4 — Upper bound on s

There is no (58, 85, 14663)-net in base 4, because

1 times m-reduction [i] would yield (58, 84, 14663)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 374 256272 852369 139135 480035 982412 736475 971660 837680 > 4⁸⁴ [i]