MinT - Best Known (129−84, 129, s)-Nets in Base 4

Best Known (129−84, 129, s)-Nets in Base 4

(129−84, 129, 56)-Net over F₄ — Constructive and digital

Digital (45, 129, 56)-net over F₄, using

t-expansion [i] based on digital (33, 129, 56)-net over F₄, using
- net from sequence [i] based on digital (33, 55)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(129−84, 129, 80)-Net over F₄ — Digital

Digital (45, 129, 80)-net over F₄, using

net from sequence [i] based on digital (45, 79)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 45 and N(F) ≥ 80, using
  - Drinfeld modules of rank 1 [i]

(129−84, 129, 355)-Net in Base 4 — Upper bound on s

There is no (45, 129, 356)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 486546 414348 722088 931200 932678 105356 943376 254609 209243 700395 116127 911906 326968 > 4¹²⁹ [i]