MinT - Best Known (130, 130+99, s)-Nets in Base 4

Best Known (130, 130+99, s)-Nets in Base 4

(130, 130+99, 130)-Net over F₄ — Constructive and digital

Digital (130, 229, 130)-net over F₄, using

t-expansion [i] based on digital (105, 229, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(130, 130+99, 256)-Net over F₄ — Digital

Digital (130, 229, 256)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(130, 130+99, 3992)-Net in Base 4 — Upper bound on s

There is no (130, 229, 3993)-net in base 4, because

1 times m-reduction [i] would yield (130, 228, 3993)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 186882 262886 782080 148043 453040 900821 534606 531936 786350 906735 428946 843056 835760 221807 680995 515414 179892 297212 005037 674018 518304 257964 383024 > 4²²⁸ [i]