MinT - Best Known (120−73, 120, s)-Nets in Base 4

Best Known (120−73, 120, s)-Nets in Base 4

(120−73, 120, 56)-Net over F₄ — Constructive and digital

Digital (47, 120, 56)-net over F₄, using

t-expansion [i] based on digital (33, 120, 56)-net over F₄, using
- net from sequence [i] based on digital (33, 55)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(120−73, 120, 81)-Net over F₄ — Digital

Digital (47, 120, 81)-net over F₄, using

t-expansion [i] based on digital (46, 120, 81)-net over F₄, using
- net from sequence [i] based on digital (46, 80)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 46 and N(F) ≥ 81, using
    - Drinfeld modules of rank 1 [i]

(120−73, 120, 436)-Net in Base 4 — Upper bound on s

There is no (47, 120, 437)-net in base 4, because

1 times m-reduction [i] would yield (47, 119, 437)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 458368 646784 906574 409032 318986 968547 040649 143045 597058 755721 577055 960015 > 4¹¹⁹ [i]