MinT - Best Known (259−96, 259, s)-Nets in Base 4

Best Known (259−96, 259, s)-Nets in Base 4

(259−96, 259, 200)-Net over F₄ — Constructive and digital

Digital (163, 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]

(259−96, 259, 475)-Net over F₄ — Digital

Digital (163, 259, 475)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(259−96, 259, 11034)-Net in Base 4 — Upper bound on s

There is no (163, 259, 11035)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 861724 081480 578887 699850 535913 453241 012467 691027 787134 166778 654172 124289 782607 882807 603461 094814 057314 517605 104306 606117 792470 294318 630427 169398 629503 597128 > 4²⁵⁹ [i]