MinT - Best Known (203−85, 203, s)-Nets in Base 4

Best Known (203−85, 203, s)-Nets in Base 4

(203−85, 203, 130)-Net over F₄ — Constructive and digital

Digital (118, 203, 130)-net over F₄, using

t-expansion [i] based on digital (105, 203, 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]

(203−85, 203, 256)-Net over F₄ — Digital

Digital (118, 203, 256)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(203−85, 203, 4293)-Net in Base 4 — Upper bound on s

There is no (118, 203, 4294)-net in base 4, because

1 times m-reduction [i] would yield (118, 202, 4294)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 41 413698 930919 814486 910334 769935 164511 383000 369610 443795 666054 993819 518634 892808 119754 931310 659301 181422 724587 907269 342960 > 4²⁰² [i]