MinT - Best Known (259−97, 259, s)-Nets in Base 4

Best Known (259−97, 259, s)-Nets in Base 4

(259−97, 259, 200)-Net over F₄ — Constructive and digital

Digital (162, 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]

(259−97, 259, 458)-Net over F₄ — Digital

Digital (162, 259, 458)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(259−97, 259, 10718)-Net in Base 4 — Upper bound on s

There is no (162, 259, 10719)-net in base 4, because

1 times m-reduction [i] would yield (162, 258, 10719)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 214727 090014 139818 979499 843571 815431 937652 409571 831078 739428 350190 275374 676994 872723 554894 975960 637299 637353 705407 709970 376977 354654 203991 181482 698851 039394 > 4²⁵⁸ [i]