MinT - Best Known (74, 159, s)-Nets in Base 4

Best Known (74, 159, s)-Nets in Base 4

(74, 159, 104)-Net over F₄ — Constructive and digital

Digital (74, 159, 104)-net over F₄, using

t-expansion [i] based on digital (73, 159, 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, 159, 112)-Net over F₄ — Digital

Digital (74, 159, 112)-net over F₄, using

t-expansion [i] based on digital (73, 159, 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, 159, 978)-Net in Base 4 — Upper bound on s

There is no (74, 159, 979)-net in base 4, because

1 times m-reduction [i] would yield (74, 158, 979)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 134292 442236 594586 586868 881257 280239 826339 727185 484932 478320 995803 228838 451889 704164 055612 507260 > 4¹⁵⁸ [i]