MinT - Best Known (208−98, 208, s)-Nets in Base 4

Best Known (208−98, 208, s)-Nets in Base 4

(208−98, 208, 130)-Net over F₄ — Constructive and digital

Digital (110, 208, 130)-net over F₄, using

t-expansion [i] based on digital (105, 208, 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]

(208−98, 208, 180)-Net over F₄ — Digital

Digital (110, 208, 180)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(208−98, 208, 2250)-Net in Base 4 — Upper bound on s

There is no (110, 208, 2251)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 172449 313983 167028 824280 834487 069682 365888 523011 074859 253308 733159 585949 032229 114242 573391 058337 999552 895217 255980 338390 782264 > 4²⁰⁸ [i]