MinT - Best Known (205−85, 205, s)-Nets in Base 4

Best Known (205−85, 205, s)-Nets in Base 4

(205−85, 205, 130)-Net over F₄ — Constructive and digital

Digital (120, 205, 130)-net over F₄, using

t-expansion [i] based on digital (105, 205, 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]

(205−85, 205, 266)-Net over F₄ — Digital

Digital (120, 205, 266)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−85, 205, 4589)-Net in Base 4 — Upper bound on s

There is no (120, 205, 4590)-net in base 4, because

1 times m-reduction [i] would yield (120, 204, 4590)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 666 419831 515987 098182 461071 253429 624196 577625 179338 215176 740932 003343 269058 679533 344683 411188 462199 273769 141300 680991 800370 > 4²⁰⁴ [i]