MinT - Best Known (210−90, 210, s)-Nets in Base 4

Best Known (210−90, 210, s)-Nets in Base 4

(210−90, 210, 130)-Net over F₄ — Constructive and digital

Digital (120, 210, 130)-net over F₄, using

t-expansion [i] based on digital (105, 210, 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]

(210−90, 210, 244)-Net over F₄ — Digital

Digital (120, 210, 244)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−90, 210, 3753)-Net in Base 4 — Upper bound on s

There is no (120, 210, 3754)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 728070 476785 297183 156010 018060 054084 741059 378079 910518 050485 473928 095118 283035 904790 767735 184681 169649 179038 490830 588440 183904 > 4²¹⁰ [i]