MinT - Best Known (111−35, 111, s)-Nets in Base 4

Best Known (111−35, 111, s)-Nets in Base 4

(111−35, 111, 240)-Net over F₄ — Constructive and digital

Digital (76, 111, 240)-net over F₄, using

t-expansion [i] based on digital (75, 111, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 37, 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]

(111−35, 111, 423)-Net over F₄ — Digital

Digital (76, 111, 423)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(111−35, 111, 18801)-Net in Base 4 — Upper bound on s

There is no (76, 111, 18802)-net in base 4, because

1 times m-reduction [i] would yield (76, 110, 18802)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 685872 340421 423572 333356 135685 383951 703263 815061 283950 837652 189005 > 4¹¹⁰ [i]