MinT - Best Known (255−127, 255, s)-Nets in Base 4

Best Known (255−127, 255, s)-Nets in Base 4

(255−127, 255, 130)-Net over F₄ — Constructive and digital

Digital (128, 255, 130)-net over F₄, using

t-expansion [i] based on digital (105, 255, 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]

(255−127, 255, 181)-Net over F₄ — Digital

Digital (128, 255, 181)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(255−127, 255, 2115)-Net in Base 4 — Upper bound on s

There is no (128, 255, 2116)-net in base 4, because

1 times m-reduction [i] would yield (128, 254, 2116)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 845 661878 966010 353311 832854 308279 822802 382017 796613 925986 142345 495133 549614 200916 361285 549987 432290 966374 435626 436589 735963 920132 096951 216761 185856 158960 > 4²⁵⁴ [i]