MinT - Best Known (162, 162+98, s)-Nets in Base 4

Best Known (162, 162+98, s)-Nets in Base 4

(162, 162+98, 200)-Net over F₄ — Constructive and digital

Digital (162, 260, 200)-net over F₄, using

t-expansion [i] based on digital (161, 260, 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]

(162, 162+98, 450)-Net over F₄ — Digital

Digital (162, 260, 450)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(162, 162+98, 9931)-Net in Base 4 — Upper bound on s

There is no (162, 260, 9932)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 433572 409085 475883 219804 352121 827676 480538 365975 514993 481345 299842 348873 746900 878181 675029 391651 046087 530267 920544 778205 825871 596939 502640 233166 867564 697420 > 4²⁶⁰ [i]