MinT - Best Known (201−112, 201, s)-Nets in Base 4

Best Known (201−112, 201, s)-Nets in Base 4

(201−112, 201, 104)-Net over F₄ — Constructive and digital

Digital (89, 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]

(201−112, 201, 129)-Net over F₄ — Digital

Digital (89, 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]

(201−112, 201, 1002)-Net in Base 4 — Upper bound on s

There is no (89, 201, 1003)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 389633 173178 254489 095659 697175 888282 432846 207608 524848 302502 271745 987111 494531 888580 286876 847816 811570 845422 315572 651420 > 4²⁰¹ [i]