MinT - Best Known (225−152, 225, s)-Nets in Base 4

Best Known (225−152, 225, s)-Nets in Base 4

(225−152, 225, 104)-Net over F₄ — Constructive and digital

Digital (73, 225, 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]

(225−152, 225, 112)-Net over F₄ — Digital

Digital (73, 225, 112)-net over F₄, using

net from sequence [i] based on digital (73, 111)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
  - Drinfeld modules of rank 1 [i]

(225−152, 225, 527)-Net in Base 4 — Upper bound on s

There is no (73, 225, 528)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3029 506616 952939 995599 974144 748193 679941 167746 599958 852299 019920 016875 020711 265204 443611 526340 341162 923366 824373 785190 794986 333824 611080 > 4²²⁵ [i]