MinT - Best Known (160−75, 160, s)-Nets in Base 4

Best Known (160−75, 160, s)-Nets in Base 4

(160−75, 160, 104)-Net over F₄ — Constructive and digital

Digital (85, 160, 104)-net over F₄, using

t-expansion [i] based on digital (73, 160, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(160−75, 160, 145)-Net over F₄ — Digital

Digital (85, 160, 145)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−75, 160, 1857)-Net in Base 4 — Upper bound on s

There is no (85, 160, 1858)-net in base 4, because

1 times m-reduction [i] would yield (85, 159, 1858)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 534665 910682 571605 950116 957463 899398 866445 918382 721531 408969 466762 843989 866402 530045 020103 697200 > 4¹⁵⁹ [i]