MinT - Best Known (200−83, 200, s)-Nets in Base 4

Best Known (200−83, 200, s)-Nets in Base 4

(200−83, 200, 130)-Net over F₄ — Constructive and digital

Digital (117, 200, 130)-net over F₄, using

t-expansion [i] based on digital (105, 200, 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]

(200−83, 200, 259)-Net over F₄ — Digital

Digital (117, 200, 259)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(200−83, 200, 4464)-Net in Base 4 — Upper bound on s

There is no (117, 200, 4465)-net in base 4, because

1 times m-reduction [i] would yield (117, 199, 4465)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 651025 815661 130722 905680 695603 023836 841548 195135 936776 012569 253029 743752 354602 882916 062357 638704 797508 727806 612367 871400 > 4¹⁹⁹ [i]