MinT - Best Known (205−83, 205, s)-Nets in Base 4

Best Known (205−83, 205, s)-Nets in Base 4

(205−83, 205, 130)-Net over F₄ — Constructive and digital

Digital (122, 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]

(205−83, 205, 287)-Net over F₄ — Digital

Digital (122, 205, 287)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−83, 205, 5292)-Net in Base 4 — Upper bound on s

There is no (122, 205, 5293)-net in base 4, because

1 times m-reduction [i] would yield (122, 204, 5293)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 663 662267 609947 602937 246686 256724 924874 825458 419722 399023 381426 354543 553557 927537 826765 996871 087653 777039 490763 570899 435120 > 4²⁰⁴ [i]