MinT - Best Known (217−130, 217, s)-Nets in Base 4

Best Known (217−130, 217, s)-Nets in Base 4

(217−130, 217, 104)-Net over F₄ — Constructive and digital

Digital (87, 217, 104)-net over F₄, using

t-expansion [i] based on digital (73, 217, 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]

(217−130, 217, 129)-Net over F₄ — Digital

Digital (87, 217, 129)-net over F₄, using

t-expansion [i] based on digital (81, 217, 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]

(217−130, 217, 801)-Net in Base 4 — Upper bound on s

There is no (87, 217, 802)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 45207 465011 885704 350165 130793 709755 831803 158835 765498 535101 216910 390831 013491 400431 615099 694514 354503 833361 374981 945834 561246 768452 > 4²¹⁷ [i]