MinT - Best Known (112, 112+37, s)-Nets in Base 4

Best Known (112, 112+37, s)-Nets in Base 4

(112, 112+37, 1028)-Net over F₄ — Constructive and digital

Digital (112, 149, 1028)-net over F₄, using

4¹ times duplication [i] based on digital (111, 148, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 37, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(112, 112+37, 1495)-Net over F₄ — Digital

Digital (112, 149, 1495)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 112+37, 224518)-Net in Base 4 — Upper bound on s

There is no (112, 149, 224519)-net in base 4, because

1 times m-reduction [i] would yield (112, 148, 224519)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 127321 627849 233786 118747 308551 647871 475455 730784 125856 144241 321768 729627 332200 504496 626064 > 4¹⁴⁸ [i]