MinT - Best Known (118, 118+45, s)-Nets in Base 4

Best Known (118, 118+45, s)-Nets in Base 4

(118, 118+45, 531)-Net over F₄ — Constructive and digital

Digital (118, 163, 531)-net over F₄, using

t-expansion [i] based on digital (117, 163, 531)-net over F₄, using
- 2 times m-reduction [i] based on digital (117, 165, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 55, 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]

(118, 118+45, 999)-Net over F₄ — Digital

Digital (118, 163, 999)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(118, 118+45, 81844)-Net in Base 4 — Upper bound on s

There is no (118, 163, 81845)-net in base 4, because

1 times m-reduction [i] would yield (118, 162, 81845)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 34 182971 779097 496724 515210 952045 279698 815807 498242 541091 437031 291588 332764 614219 703010 280365 639104 > 4¹⁶² [i]