MinT - Best Known (186−102, 186, s)-Nets in Base 4

Best Known (186−102, 186, s)-Nets in Base 4

(186−102, 186, 104)-Net over F₄ — Constructive and digital

Digital (84, 186, 104)-net over F₄, using

t-expansion [i] based on digital (73, 186, 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]

(186−102, 186, 129)-Net over F₄ — Digital

Digital (84, 186, 129)-net over F₄, using

t-expansion [i] based on digital (81, 186, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(186−102, 186, 997)-Net in Base 4 — Upper bound on s

There is no (84, 186, 998)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9947 107373 658553 563129 233387 453963 681665 543877 268967 447050 725778 133083 913848 906152 073813 957944 198948 217220 403320 > 4¹⁸⁶ [i]