MinT - Best Known (116, 116+40, s)-Nets in Base 4

Best Known (116, 116+40, s)-Nets in Base 4

(116, 116+40, 531)-Net over F₄ — Constructive and digital

Digital (116, 156, 531)-net over F₄, using

t-expansion [i] based on digital (115, 156, 531)-net over F₄, using
- 6 times m-reduction [i] based on digital (115, 162, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 54, 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]

(116, 116+40, 576)-Net in Base 4 — Constructive

(116, 156, 576)-net in base 4, using

t-expansion [i] based on (115, 156, 576)-net in base 4, using
- trace code for nets [i] based on (11, 52, 192)-net in base 64, using
  - 4 times m-reduction [i] based on (11, 56, 192)-net in base 64, using
    - base change [i] based on digital (3, 48, 192)-net over F₁₂₈, using
      - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(116, 116+40, 1333)-Net over F₄ — Digital

Digital (116, 156, 1333)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(116, 116+40, 137468)-Net in Base 4 — Upper bound on s

There is no (116, 156, 137469)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8344 826674 035694 757714 092952 930722 925160 470477 243749 946755 756372 165929 460382 062834 612257 013579 > 4¹⁵⁶ [i]