MinT - Best Known (87, 87+114, s)-Nets in Base 4

Best Known (87, 87+114, s)-Nets in Base 4

(87, 87+114, 104)-Net over F₄ — Constructive and digital

Digital (87, 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]

(87, 87+114, 129)-Net over F₄ — Digital

Digital (87, 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]

(87, 87+114, 930)-Net in Base 4 — Upper bound on s

There is no (87, 201, 931)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 378701 672090 803625 135886 429941 738383 869831 153142 227718 486234 591375 057391 643110 605619 705737 098852 711993 651984 449033 127456 > 4²⁰¹ [i]