MinT - Best Known (159−82, 159, s)-Nets in Base 4

Best Known (159−82, 159, s)-Nets in Base 4

(159−82, 159, 104)-Net over F₄ — Constructive and digital

Digital (77, 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]

(159−82, 159, 112)-Net over F₄ — Digital

Digital (77, 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]

(159−82, 159, 1129)-Net in Base 4 — Upper bound on s

There is no (77, 159, 1130)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 538128 915024 924110 677228 338214 107907 435659 306323 642204 205457 697801 644785 095135 472906 478016 845441 > 4¹⁵⁹ [i]