MinT - Best Known (222−109, 222, s)-Nets in Base 4

Best Known (222−109, 222, s)-Nets in Base 4

(222−109, 222, 130)-Net over F₄ — Constructive and digital

Digital (113, 222, 130)-net over F₄, using

t-expansion [i] based on digital (105, 222, 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]

(222−109, 222, 167)-Net over F₄ — Digital

Digital (113, 222, 167)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(222−109, 222, 1990)-Net in Base 4 — Upper bound on s

There is no (113, 222, 1991)-net in base 4, because

1 times m-reduction [i] would yield (113, 221, 1991)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 620665 256982 940602 930318 557358 289113 910566 867091 663251 001184 825252 147410 694394 119590 757599 240371 611737 884792 738951 786973 656730 358756 > 4²²¹ [i]