MinT - Best Known (103, 103+41, s)-Nets in Base 4

Best Known (103, 103+41, s)-Nets in Base 4

(103, 103+41, 531)-Net over F₄ — Constructive and digital

Digital (103, 144, 531)-net over F₄, using

trace code for nets [i] based on digital (7, 48, 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]

(103, 103+41, 793)-Net over F₄ — Digital

Digital (103, 144, 793)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(103, 103+41, 55819)-Net in Base 4 — Upper bound on s

There is no (103, 144, 55820)-net in base 4, because

1 times m-reduction [i] would yield (103, 143, 55820)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 124 340352 530024 984697 266492 665891 397960 073309 572300 733013 167431 926561 777526 946064 636864 > 4¹⁴³ [i]