MinT - Best Known (209−91, 209, s)-Nets in Base 4

Best Known (209−91, 209, s)-Nets in Base 4

(209−91, 209, 130)-Net over F₄ — Constructive and digital

Digital (118, 209, 130)-net over F₄, using

t-expansion [i] based on digital (105, 209, 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]

(209−91, 209, 231)-Net over F₄ — Digital

Digital (118, 209, 231)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(209−91, 209, 3526)-Net in Base 4 — Upper bound on s

There is no (118, 209, 3527)-net in base 4, because

1 times m-reduction [i] would yield (118, 208, 3527)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 169448 841991 755377 410337 746267 020551 455769 886237 428699 992168 106290 621927 427950 398621 453838 893437 518314 512511 124120 430023 425712 > 4²⁰⁸ [i]