MinT - Best Known (114, 231, s)-Nets in Base 4

Best Known (114, 231, s)-Nets in Base 4

(114, 231, 130)-Net over F₄ — Constructive and digital

Digital (114, 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]

(114, 231, 165)-Net over F₄ — Digital

Digital (114, 231, 165)-net over F₄, using

t-expansion [i] based on digital (109, 231, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(114, 231, 1778)-Net in Base 4 — Upper bound on s

There is no (114, 231, 1779)-net in base 4, because

1 times m-reduction [i] would yield (114, 230, 1779)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 977734 151643 403263 556645 404314 146234 708626 784265 217835 070646 848342 812048 834722 424214 296689 382734 621148 530180 343457 251363 017345 103913 990120 > 4²³⁰ [i]