MinT - Best Known (111, 111+73, s)-Nets in Base 4

Best Known (111, 111+73, s)-Nets in Base 4

(111, 111+73, 130)-Net over F₄ — Constructive and digital

Digital (111, 184, 130)-net over F₄, using

t-expansion [i] based on digital (105, 184, 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+73, 279)-Net over F₄ — Digital

Digital (111, 184, 279)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+73, 5441)-Net in Base 4 — Upper bound on s

There is no (111, 184, 5442)-net in base 4, because

1 times m-reduction [i] would yield (111, 183, 5442)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 150 482722 675376 338207 470845 198576 725271 279392 202186 446898 183645 408276 767287 781714 260028 141862 419950 151612 686160 > 4¹⁸³ [i]