MinT - Best Known (248−114, 248, s)-Nets in Base 4

Best Known (248−114, 248, s)-Nets in Base 4

(248−114, 248, 130)-Net over F₄ — Constructive and digital

Digital (134, 248, 130)-net over F₄, using

t-expansion [i] based on digital (105, 248, 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]

(248−114, 248, 227)-Net over F₄ — Digital

Digital (134, 248, 227)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−114, 248, 3017)-Net in Base 4 — Upper bound on s

There is no (134, 248, 3018)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 205351 321609 904007 412776 714256 263476 255226 039802 927221 694857 893490 571139 183327 808233 856233 983978 032523 181866 535277 196853 283427 301163 394654 275452 493604 > 4²⁴⁸ [i]