MinT - Best Known (190−111, 190, s)-Nets in Base 4

Best Known (190−111, 190, s)-Nets in Base 4

(190−111, 190, 104)-Net over F₄ — Constructive and digital

Digital (79, 190, 104)-net over F₄, using

t-expansion [i] based on digital (73, 190, 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]

(190−111, 190, 112)-Net over F₄ — Digital

Digital (79, 190, 112)-net over F₄, using

t-expansion [i] based on digital (73, 190, 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]

(190−111, 190, 789)-Net in Base 4 — Upper bound on s

There is no (79, 190, 790)-net in base 4, because

1 times m-reduction [i] would yield (79, 189, 790)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 651758 617255 819067 049527 680660 079295 299024 764621 364391 748363 513128 177941 238486 043132 836089 419540 764018 344708 619520 > 4¹⁸⁹ [i]