MinT - Best Known (111, 111+99, s)-Nets in Base 4

Best Known (111, 111+99, s)-Nets in Base 4

(111, 111+99, 130)-Net over F₄ — Constructive and digital

Digital (111, 210, 130)-net over F₄, using

t-expansion [i] based on digital (105, 210, 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]

(111, 111+99, 181)-Net over F₄ — Digital

Digital (111, 210, 181)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+99, 2315)-Net in Base 4 — Upper bound on s

There is no (111, 210, 2316)-net in base 4, because

1 times m-reduction [i] would yield (111, 209, 2316)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 679314 954672 281787 622521 681474 596589 980578 695615 096347 654966 923523 214003 716548 722162 672507 130720 618323 535213 872972 531008 326000 > 4²⁰⁹ [i]