MinT - Best Known (105, 105+101, s)-Nets in Base 4

Best Known (105, 105+101, s)-Nets in Base 4

(105, 105+101, 130)-Net over F₄ — Constructive and digital

Digital (105, 206, 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]

(105, 105+101, 157)-Net over F₄ — Digital

Digital (105, 206, 157)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 105+101, 1868)-Net in Base 4 — Upper bound on s

There is no (105, 206, 1869)-net in base 4, because

1 times m-reduction [i] would yield (105, 205, 1869)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2646 881266 765789 705476 573258 841960 021267 928441 913723 525194 160203 023469 085265 272135 289447 524123 021948 520644 432153 555568 496296 > 4²⁰⁵ [i]