MinT - Best Known (80, 249, s)-Nets in Base 4

Best Known (80, 249, s)-Nets in Base 4

(80, 249, 104)-Net over F₄ — Constructive and digital

Digital (80, 249, 104)-net over F₄, using

t-expansion [i] based on digital (73, 249, 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]

(80, 249, 112)-Net over F₄ — Digital

Digital (80, 249, 112)-net over F₄, using

t-expansion [i] based on digital (73, 249, 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]

(80, 249, 573)-Net in Base 4 — Upper bound on s

There is no (80, 249, 574)-net in base 4, because

1 times m-reduction [i] would yield (80, 248, 574)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 209557 148924 471216 908448 383105 113152 147924 999038 893423 785696 656116 015419 067805 208192 733247 037175 787858 126188 973010 818200 067253 708622 402297 171773 017240 > 4²⁴⁸ [i]