MinT - Best Known (205−87, 205, s)-Nets in Base 4

Best Known (205−87, 205, s)-Nets in Base 4

(205−87, 205, 130)-Net over F₄ — Constructive and digital

Digital (118, 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]

(205−87, 205, 247)-Net over F₄ — Digital

Digital (118, 205, 247)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−87, 205, 4007)-Net in Base 4 — Upper bound on s

There is no (118, 205, 4008)-net in base 4, because

1 times m-reduction [i] would yield (118, 204, 4008)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 667 304282 398112 962200 621830 354032 621666 448075 763221 913714 490777 643441 588154 312402 389729 504305 510103 695117 123514 322171 427120 > 4²⁰⁴ [i]