MinT - Best Known (255−93, 255, s)-Nets in Base 4

Best Known (255−93, 255, s)-Nets in Base 4

(255−93, 255, 200)-Net over F₄ — Constructive and digital

Digital (162, 255, 200)-net over F₄, using

t-expansion [i] based on digital (161, 255, 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]

(255−93, 255, 496)-Net over F₄ — Digital

Digital (162, 255, 496)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(255−93, 255, 12624)-Net in Base 4 — Upper bound on s

There is no (162, 255, 12625)-net in base 4, because

1 times m-reduction [i] would yield (162, 254, 12625)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 838 225405 797867 109211 305227 206032 067899 456323 586856 607624 250700 232804 144085 331892 305939 565454 406950 740487 055845 982287 448637 163767 290223 517587 873821 961616 > 4²⁵⁴ [i]