MinT - Best Known (208−94, 208, s)-Nets in Base 4

Best Known (208−94, 208, s)-Nets in Base 4

(208−94, 208, 130)-Net over F₄ — Constructive and digital

Digital (114, 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]

(208−94, 208, 204)-Net over F₄ — Digital

Digital (114, 208, 204)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(208−94, 208, 2789)-Net in Base 4 — Upper bound on s

There is no (114, 208, 2790)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 171761 151869 489506 039669 419908 335767 602866 289933 079484 707154 412371 900453 744096 099862 261964 798979 210162 087861 099525 388452 118752 > 4²⁰⁸ [i]