MinT - Best Known (82, 205, s)-Nets in Base 4

Best Known (82, 205, s)-Nets in Base 4

(82, 205, 104)-Net over F₄ — Constructive and digital

Digital (82, 205, 104)-net over F₄, using

t-expansion [i] based on digital (73, 205, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(82, 205, 129)-Net over F₄ — Digital

Digital (82, 205, 129)-net over F₄, using

t-expansion [i] based on digital (81, 205, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(82, 205, 760)-Net in Base 4 — Upper bound on s

There is no (82, 205, 761)-net in base 4, because

1 times m-reduction [i] would yield (82, 204, 761)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 664 123144 707659 416715 008744 615401 403507 192844 042131 355110 903734 088321 463885 129924 422923 081694 864936 948323 574954 980537 108352 > 4²⁰⁴ [i]