MinT - Best Known (112, 112+45, s)-Nets in Base 4

Best Known (112, 112+45, s)-Nets in Base 4

(112, 112+45, 531)-Net over F₄ — Constructive and digital

Digital (112, 157, 531)-net over F₄, using

4¹ times duplication [i] based on digital (111, 156, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 52, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(112, 112+45, 829)-Net over F₄ — Digital

Digital (112, 157, 829)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 112+45, 56072)-Net in Base 4 — Upper bound on s

There is no (112, 157, 56073)-net in base 4, because

1 times m-reduction [i] would yield (112, 156, 56073)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8346 843472 931816 785715 115408 425579 475244 398970 383133 885810 384131 488344 763436 782493 690324 948928 > 4¹⁵⁶ [i]