MinT - Best Known (114, 114+40, s)-Nets in Base 4

Best Known (114, 114+40, s)-Nets in Base 4

(114, 114+40, 531)-Net over F₄ — Constructive and digital

Digital (114, 154, 531)-net over F₄, using

t-expansion [i] based on digital (113, 154, 531)-net over F₄, using
- 5 times m-reduction [i] based on digital (113, 159, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 53, 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]

(114, 114+40, 576)-Net in Base 4 — Constructive

(114, 154, 576)-net in base 4, using

4¹ times duplication [i] based on (113, 153, 576)-net in base 4, using
- trace code for nets [i] based on (11, 51, 192)-net in base 64, using
  - 5 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]

(114, 114+40, 1243)-Net over F₄ — Digital

Digital (114, 154, 1243)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(114, 114+40, 119670)-Net in Base 4 — Upper bound on s

There is no (114, 154, 119671)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 521 497389 408759 545295 553889 492075 121515 931828 491094 064342 301004 076147 346107 441236 803695 969861 > 4¹⁵⁴ [i]