MinT - Best Known (136−43, 136, s)-Nets in Base 4

Best Known (136−43, 136, s)-Nets in Base 4

(136−43, 136, 240)-Net over F₄ — Constructive and digital

Digital (93, 136, 240)-net over F₄, using

2 times m-reduction [i] based on digital (93, 138, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 46, 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]

(136−43, 136, 489)-Net over F₄ — Digital

Digital (93, 136, 489)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−43, 136, 21449)-Net in Base 4 — Upper bound on s

There is no (93, 136, 21450)-net in base 4, because

1 times m-reduction [i] would yield (93, 135, 21450)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1898 448020 063475 316629 717038 186988 202074 517653 634728 889536 332470 745262 361955 774536 > 4¹³⁵ [i]