MinT - Best Known (201−119, 201, s)-Nets in Base 4

Best Known (201−119, 201, s)-Nets in Base 4

(201−119, 201, 104)-Net over F₄ — Constructive and digital

Digital (82, 201, 104)-net over F₄, using

t-expansion [i] based on digital (73, 201, 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]

(201−119, 201, 129)-Net over F₄ — Digital

Digital (82, 201, 129)-net over F₄, using

t-expansion [i] based on digital (81, 201, 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]

(201−119, 201, 788)-Net in Base 4 — Upper bound on s

There is no (82, 201, 789)-net in base 4, because

1 times m-reduction [i] would yield (82, 200, 789)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 736557 186798 981692 403297 735103 508384 526579 938121 472906 141806 453339 552651 688609 407695 718444 202416 784075 723342 741634 775680 > 4²⁰⁰ [i]