MinT - Best Known (229−111, 229, s)-Nets in Base 4

Best Known (229−111, 229, s)-Nets in Base 4

(229−111, 229, 130)-Net over F₄ — Constructive and digital

Digital (118, 229, 130)-net over F₄, using

t-expansion [i] based on digital (105, 229, 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]

(229−111, 229, 179)-Net over F₄ — Digital

Digital (118, 229, 179)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−111, 229, 2182)-Net in Base 4 — Upper bound on s

There is no (118, 229, 2183)-net in base 4, because

1 times m-reduction [i] would yield (118, 228, 2183)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 187566 890897 784216 069746 247359 343386 574905 846946 142959 729324 239640 065739 757880 653300 339602 720082 991357 647888 114261 874270 946653 848967 989216 > 4²²⁸ [i]