MinT - Best Known (137−96, 137, s)-Nets in Base 4

Best Known (137−96, 137, s)-Nets in Base 4

(137−96, 137, 56)-Net over F₄ — Constructive and digital

Digital (41, 137, 56)-net over F₄, using

t-expansion [i] based on digital (33, 137, 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]

(137−96, 137, 75)-Net over F₄ — Digital

Digital (41, 137, 75)-net over F₄, using

t-expansion [i] based on digital (40, 137, 75)-net over F₄, using
- net from sequence [i] based on digital (40, 74)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 40 and N(F) ≥ 75, using
    - Drinfeld modules of rank 1 [i]

(137−96, 137, 288)-Net in Base 4 — Upper bound on s

There is no (41, 137, 289)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 31057 688102 082573 002023 428042 136044 657366 572915 252200 511906 598968 685037 029101 478544 > 4¹³⁷ [i]