MinT - Best Known (205−97, 205, s)-Nets in Base 4

Best Known (205−97, 205, s)-Nets in Base 4

(205−97, 205, 130)-Net over F₄ — Constructive and digital

Digital (108, 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]

(205−97, 205, 175)-Net over F₄ — Digital

Digital (108, 205, 175)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−97, 205, 2222)-Net in Base 4 — Upper bound on s

There is no (108, 205, 2223)-net in base 4, because

1 times m-reduction [i] would yield (108, 204, 2223)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 669 504535 797172 464893 376366 360285 958397 254669 443744 819497 875130 128994 079755 382026 311005 531371 421431 119115 792684 330152 537720 > 4²⁰⁴ [i]