MinT - Best Known (224−101, 224, s)-Nets in Base 4

Best Known (224−101, 224, s)-Nets in Base 4

(224−101, 224, 130)-Net over F₄ — Constructive and digital

Digital (123, 224, 130)-net over F₄, using

t-expansion [i] based on digital (105, 224, 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]

(224−101, 224, 220)-Net over F₄ — Digital

Digital (123, 224, 220)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−101, 224, 3104)-Net in Base 4 — Upper bound on s

There is no (123, 224, 3105)-net in base 4, because

1 times m-reduction [i] would yield (123, 223, 3105)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 182 247334 300518 543141 350784 284537 504633 087522 151925 857707 069600 899893 252258 177780 605261 900408 886435 817035 762584 776012 477310 074722 996736 > 4²²³ [i]