MinT - Best Known (74, 74+177, s)-Nets in Base 4

Best Known (74, 74+177, s)-Nets in Base 4

(74, 74+177, 104)-Net over F₄ — Constructive and digital

Digital (74, 251, 104)-net over F₄, using

t-expansion [i] based on digital (73, 251, 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]

(74, 74+177, 112)-Net over F₄ — Digital

Digital (74, 251, 112)-net over F₄, using

t-expansion [i] based on digital (73, 251, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(74, 74+177, 504)-Net in Base 4 — Upper bound on s

There is no (74, 251, 505)-net in base 4, because

1 times m-reduction [i] would yield (74, 250, 505)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 450649 115398 331604 653219 224478 399755 499538 868480 522467 981544 221604 436652 977039 230581 570668 146239 930938 529371 822774 868597 157867 301198 578696 657141 055599 > 4²⁵⁰ [i]