MinT - Best Known (259−95, 259, s)-Nets in Base 4

Best Known (259−95, 259, s)-Nets in Base 4

(259−95, 259, 200)-Net over F₄ — Constructive and digital

Digital (164, 259, 200)-net over F₄, using

t-expansion [i] based on digital (161, 259, 200)-net over F₄, using
- net from sequence [i] based on digital (161, 199)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 161 and N(F) ≥ 200, using
    - F₇ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(259−95, 259, 493)-Net over F₄ — Digital

Digital (164, 259, 493)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(259−95, 259, 12318)-Net in Base 4 — Upper bound on s

There is no (164, 259, 12319)-net in base 4, because

1 times m-reduction [i] would yield (164, 258, 12319)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 215263 020339 470682 534566 930371 087127 751992 718024 280930 216506 881462 904263 541649 168236 020394 623071 394240 930931 796767 057116 036734 675706 754809 491880 056629 798400 > 4²⁵⁸ [i]