MinT - Best Known (120, 120+111, s)-Nets in Base 4

Best Known (120, 120+111, s)-Nets in Base 4

(120, 120+111, 130)-Net over F₄ — Constructive and digital

Digital (120, 231, 130)-net over F₄, using

t-expansion [i] based on digital (105, 231, 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]

(120, 120+111, 185)-Net over F₄ — Digital

Digital (120, 231, 185)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(120, 120+111, 2297)-Net in Base 4 — Upper bound on s

There is no (120, 231, 2298)-net in base 4, because

1 times m-reduction [i] would yield (120, 230, 2298)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 988669 198000 578087 662615 020969 305196 828756 944918 843229 654153 003730 832936 860238 407588 383204 993265 602433 804355 364261 779688 257518 854394 762780 > 4²³⁰ [i]