MinT - Best Known (209−101, 209, s)-Nets in Base 4

Best Known (209−101, 209, s)-Nets in Base 4

(209−101, 209, 130)-Net over F₄ — Constructive and digital

Digital (108, 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]

(209−101, 209, 166)-Net over F₄ — Digital

Digital (108, 209, 166)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(209−101, 209, 2034)-Net in Base 4 — Upper bound on s

There is no (108, 209, 2035)-net in base 4, because

1 times m-reduction [i] would yield (108, 208, 2035)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 170948 439520 144329 892396 381085 665180 816448 615540 839937 131902 039601 519752 332775 102002 763996 535139 791124 410080 921693 393752 252575 > 4²⁰⁸ [i]